muHVT: Predicting Cells with Layers using predictLayerHVT

Zubin Dowlaty, Srinivasan Sudarsanam, Somya Shambhawi

2023-06-29

1 Abstract

The muHVT package is a collection of R functions to facilitate building topology preserving maps for rich multivariate data analysis. Tending towards a big data preponderance, a large number of rows. A collection of R functions for this typical workflow is organized below:

  1. Data Compression: Vector quantization (VQ), HVQ (hierarchical vector quantization) using means or medians. This step compresses the rows (long data frame) using a compression objective.

  2. Data Projection: Dimension projection of the compressed cells to 1D,2D or 3D with the Sammons Non-linear Algorithm. This step creates topology preserving map (also called as embedding) coordinates into the desired output dimension.

  3. Tessellation: Create cells required for object visualization using the Voronoi Tessellation method, package includes heatmap plots for hierarchical Voronoi tessellations (HVT). This step enables data insights, visualization, and interaction with the topology preserving map. Useful for semi-supervised tasks.

  4. Prediction: Scoring new data sets and recording their assignment using the map objects from the above steps, in a sequence of maps if required.

2 Example: muHVT with the Personal Computer dataset

Data Understanding

In this vignette, we will use the Prices of Personal Computers dataset. This dataset contains 6259 observations and 6 features. The dataset observes the price from 1993 to 1995 of 486 personal computers in the US. The variables are price, speed, hd, ram, screen and ads.

Here, we load the data and store into a variable computers.

set.seed(240)
# Load data from csv files
computers <- read.csv("https://raw.githubusercontent.com/Mu-Sigma/muHVT/master/vignettes/sample_dataset/Computers.csv")

Raw Personal Computers Dataset

The Computers dataset includes the following columns:

Let’s explore the Personal Computers Dataset containing (6259 points). For the shake of brevity we are displaying first six rows.

Table(head(computers), scroll = T, limit = 20)
X price speed hd ram screen cd multi premium ads trend
1 1499 25 80 4 14 no no yes 94 1
2 1795 33 85 2 14 no no yes 94 1
3 1595 25 170 4 15 no no yes 94 1
4 1849 25 170 8 14 no no no 94 1
5 3295 33 340 16 14 no no yes 94 1
6 3695 66 340 16 14 no no yes 94 1

Now, let us check the structure of the data and analyse its summary.

str(computers)
#> 'data.frame':    6259 obs. of  11 variables:
#>  $ X      : int  1 2 3 4 5 6 7 8 9 10 ...
#>  $ price  : int  1499 1795 1595 1849 3295 3695 1720 1995 2225 2575 ...
#>  $ speed  : int  25 33 25 25 33 66 25 50 50 50 ...
#>  $ hd     : int  80 85 170 170 340 340 170 85 210 210 ...
#>  $ ram    : int  4 2 4 8 16 16 4 2 8 4 ...
#>  $ screen : int  14 14 15 14 14 14 14 14 14 15 ...
#>  $ cd     : chr  "no" "no" "no" "no" ...
#>  $ multi  : chr  "no" "no" "no" "no" ...
#>  $ premium: chr  "yes" "yes" "yes" "no" ...
#>  $ ads    : int  94 94 94 94 94 94 94 94 94 94 ...
#>  $ trend  : int  1 1 1 1 1 1 1 1 1 1 ...
summary(computers)
#>        X            price          speed              hd        
#>  Min.   :   1   Min.   : 949   Min.   : 25.00   Min.   :  80.0  
#>  1st Qu.:1566   1st Qu.:1794   1st Qu.: 33.00   1st Qu.: 214.0  
#>  Median :3130   Median :2144   Median : 50.00   Median : 340.0  
#>  Mean   :3130   Mean   :2220   Mean   : 52.01   Mean   : 416.6  
#>  3rd Qu.:4694   3rd Qu.:2595   3rd Qu.: 66.00   3rd Qu.: 528.0  
#>  Max.   :6259   Max.   :5399   Max.   :100.00   Max.   :2100.0  
#>       ram             screen           cd               multi          
#>  Min.   : 2.000   Min.   :14.00   Length:6259        Length:6259       
#>  1st Qu.: 4.000   1st Qu.:14.00   Class :character   Class :character  
#>  Median : 8.000   Median :14.00   Mode  :character   Mode  :character  
#>  Mean   : 8.287   Mean   :14.61                                        
#>  3rd Qu.: 8.000   3rd Qu.:15.00                                        
#>  Max.   :32.000   Max.   :17.00                                        
#>    premium               ads            trend      
#>  Length:6259        Min.   : 39.0   Min.   : 1.00  
#>  Class :character   1st Qu.:162.5   1st Qu.:10.00  
#>  Mode  :character   Median :246.0   Median :16.00  
#>                     Mean   :221.3   Mean   :15.93  
#>                     3rd Qu.:275.0   3rd Qu.:21.50  
#>                     Max.   :339.0   Max.   :35.00

Let us first split the data into train and test. We will randomly select 80% of the data for training and remaining as testing.


num_rows <- nrow(computers)
set.seed(123)
train_indices <- sample(1:num_rows, 0.8 * num_rows)
trainComputers <- computers[train_indices, ]
testComputers <- computers[-train_indices, ]

K-means is not suitable for factor variables as the sample space for factor variables is discrete. A Euclidean distance function on such a space isn’t really meaningful. Hence, we will delete the factor variables(X, cd, multi, premium, trend) in our dataset.

trainComputers <-
  trainComputers %>% dplyr::select(-c(X, cd, multi, premium, trend))
testComputers <-
  testComputers %>% dplyr::select(-c(X, cd, multi, premium, trend))

Raw Training Dataset

Now, lets have a look at the randomly selected raw training dataset containing (5007 data points). For the sake of brevity we are displaying first six rows.

trainComputers_data <- trainComputers %>% as.data.frame() %>% round(4)
trainComputers_data$Row.No <- as.numeric(row.names(trainComputers_data))
trainComputers_data <- trainComputers_data %>% dplyr::select(Row.No,price,speed,hd,ram,screen,ads)
row.names(trainComputers_data) <- NULL
Table(head(trainComputers_data))
Row.No price speed hd ram screen ads
2463 2799 50 230 8 15 216
2511 2197 33 270 4 14 216
2227 2744 50 340 8 17 275
526 2999 66 245 16 15 139
4291 1974 33 200 4 14 248
2986 2490 33 528 16 14 267

Raw Testing Dataset

Now, lets have a look at the randomly selected raw testing dataset containing (1252 data points). For the sake of brevity we are displaying first six rows.

#testComputers <- scale(testComputers, center = scale_attr$`scaled:center`, scale = scale_attr$`scaled:scale`) 
testComputers_data <- testComputers %>% as.data.frame() %>% round(4)
testComputers_data$Row.No <- as.numeric(row.names(testComputers_data))
testComputers_data <- testComputers_data %>% dplyr::select(Row.No,price,speed,hd,ram,screen,ads)
rownames(testComputers_data) <- NULL
Table(head(testComputers_data))
Row.No price speed hd ram screen ads
3 1595 25 170 4 15 94
4 1849 25 170 8 14 94
7 1720 25 170 4 14 94
10 2575 50 210 4 15 94
11 2195 33 170 8 15 94
14 2295 25 245 8 14 94

3 Map A : Base Compressed Map

Let us try to visualize the compressed Map A from the flow diagram below.

Figure 1: Flow map with highlighted bounding box in red around compressed map A

Figure 1: Flow map with highlighted bounding box in red around compressed map A

This package can perform vector quantization using the following algorithms -

For more information on vector quantization, refer the following link.

The HVT function constructs highly compressed hierarchical Voronoi tessellations. The raw data is first scaled and this scaled data is supplied as input to the vector quantization algorithm. The vector quantization algorithm compresses the dataset until a user-defined compression percentage/rate is achieved using a parameter called quantization error which acts as a threshold and determines the compression percentage. It means that for a given user-defined compression percentage we get the ‘n’ number of cells, then all of these cells formed will have a quantization error less than the threshold quantization error.

Let’s try to comprehend the HVT function first before moving ahead.

HVT(
  dataset,
  min_compression_perc,
  n_cells,
  depth,
  quant.err,
  distance_metric = c("L1_Norm", "L2_Norm"),
  error_metric = c("mean", "max"),
  quant_method = c("kmeans", "kmedoids"),
  normalize = TRUE,
  diagnose = FALSE,
  hvt_validation = FALSE,
  train_validation_split_ratio = 0.8
)

Each of the parameters have been explained below :

We will use the HVT function to compress our data while preserving essential features of the dataset. Our goal is to achieve data compression upto atleast 80%. In situations where the compression ratio does not meet the desired target, we can explore adjusting the model parameters as a potential solution. This involves making modifications to parameters such as the quantization error threshold or increasing the number of cells and then rerunning the HVT function again.

In our example we will iteratively increase the number of cells until the desired compression percentage is reached instead of increasing the quantization threshold because it may reduce the level of detail captured in the data representation

First, we will construct map A by using the below mentioned model parameters.

3.0.1 Iteration 1:

We will pass the below mentioned model parameters along with training dataset (containing 5007 data poits) to HVT function.

Model Parameters

set.seed(240)
map_A <- list()
map_A  <- muHVT::HVT(
  trainComputers,
  n_cells = 200,
  depth = 1,
  quant.err = 0.2,
  projection.scale = 10,
  normalize = T,
  distance_metric = "L1_Norm",
  error_metric = "max",
  quant_method = "kmeans"
)

Let’s checkout the compression summary with n_cells set to 200.

compressionSummaryTable(map_A[[3]]$compression_summary)
segmentLevel noOfCells noOfCellsBelowQuantizationError percentOfCellsBelowQuantizationErrorThreshold parameters
1 200 83 0.42 n_cells: 200 quant.err: 0.2 distance_metric: L1_Norm error_metric: max quant_method: kmeans

As it can be seen from the table above, 42% of cells have reached the quantization threshold error. Therefore we can further subdivide the cells by increasing the n_cells parameters and then see if desired compression (80%) is reached

3.0.2 Iteration 2:

Since, we are yet to achive atleast 80% compression. Let’s try to compress again using the below mentioned set of model parameters and the Computers training dataset (containing 5007 data points) .

Model Parameters

map_A <- list()
map_A <-muHVT::HVT(trainComputers,
                n_cells = 440,
                quant.err = 0.2,
                depth = 1,
                distance_metric = "L1_Norm",
                error_metric = "max",
                quant_method = "kmeans",
                normalize = T)

As per the manual, map_A[[3]] gives us detailed information about the hierarchical vector quantized data. map_A[[3]][['summary']] gives a nice tabular data containing no of points, Quantization Error and the codebook.

The datatable displayed below is the summary from map A showing Cell.ID, Centroids and Quantization Error for each of the 440 cells.

summaryTable(map_A[[3]]$summary,scroll = T,limit = 500)
Segment.Level Segment.Parent Segment.Child n Cell.ID Quant.Error price speed hd ram screen ads
1 1 1 7 46 0.08 -0.76 -0.89 -0.88 -0.76 -0.67 1.57
1 1 2 10 108 0.08 -0.80 -0.89 -0.16 -0.76 -0.67 0.67
1 1 3 15 223 0.12 0.37 -0.89 -0.72 -0.05 0.43 -1.65
1 1 4 11 54 0.07 -1.50 -0.89 -0.75 -0.76 -0.67 0.62
1 1 5 8 146 0.13 -0.31 0.68 -0.95 -0.89 -0.67 -0.14
1 1 6 11 150 0.16 -0.66 0.68 -0.78 -0.79 -0.67 -0.73
1 1 7 11 170 0.1 0.03 -1.24 -0.13 -0.05 -0.67 0.38
1 1 8 8 334 0.15 0.62 2.30 0.08 -0.05 0.43 0.04
1 1 9 8 114 0.07 -0.16 0.68 -1.19 -1.11 -0.67 0.87
1 1 10 7 248 0.17 0.51 -0.08 0.34 -0.05 -0.67 -0.30
1 1 11 9 140 0.12 -0.01 0.68 -1.15 -1.00 -0.67 0.33
1 1 12 7 219 0.14 -1.36 0.24 0.46 -0.05 -0.67 -0.74
1 1 13 9 271 0.05 -1.08 0.68 0.49 -0.05 0.43 -0.84
1 1 14 19 109 0.06 -0.31 -0.89 -0.74 -0.76 -0.67 0.38
1 1 15 6 176 0.08 -0.72 -0.89 -0.07 -0.05 0.43 0.72
1 1 16 17 332 0.14 0.42 2.30 0.10 -0.05 0.43 1.50
1 1 17 12 18 0.05 -1.21 -1.27 -1.19 -1.11 -0.67 0.97
1 1 18 19 149 0.16 -0.68 -0.08 -0.46 -0.76 0.43 0.79
1 1 19 17 428 0.35 0.18 2.30 2.53 1.37 0.43 -2.22
1 1 20 20 320 0.36 0.82 -0.16 -0.09 -0.12 2.64 0.71
1 1 21 3 305 0.18 2.27 -0.35 -0.01 -0.05 -0.67 -1.32
1 1 22 7 227 0.1 -0.51 -0.89 0.45 -0.05 0.43 -0.47
1 1 23 10 178 0.12 0.00 0.68 -0.86 -0.76 -0.67 -0.90
1 1 24 9 365 0.1 0.68 -0.08 1.20 1.37 0.43 -0.36
1 1 25 5 14 0.11 -1.99 -0.89 -0.96 -1.11 -0.67 0.18
1 1 26 3 411 0.05 1.25 -0.89 2.29 2.79 0.43 0.57
1 1 27 18 122 0.15 -0.18 -0.98 -0.85 -0.76 0.43 0.68
1 1 28 15 189 0.11 0.40 -0.92 0.03 -0.05 -0.67 0.87
1 1 29 11 107 0.11 -0.49 -0.96 -0.88 -0.76 -0.67 -0.64
1 1 30 7 423 0.47 3.55 0.12 2.51 1.37 -0.67 0.44
1 1 31 14 90 0.05 -0.63 -0.89 -0.79 -0.76 -0.67 0.58
1 1 32 22 430 0.24 0.63 0.75 3.07 2.79 0.43 -2.27
1 1 33 5 390 0.3 1.37 -0.89 3.73 -0.19 -0.45 0.70
1 1 34 25 101 0.18 -0.85 -0.97 -0.71 -0.76 0.43 0.84
1 1 35 11 425 0.07 0.15 2.30 1.70 1.37 0.43 -2.39
1 1 36 10 358 0.05 0.24 -0.89 1.20 1.37 0.43 -0.84
1 1 37 16 166 0.11 0.03 0.68 -1.08 -0.78 -0.67 -1.65
1 1 38 13 45 0.05 -0.91 -0.89 -1.19 -1.11 -0.67 0.42
1 1 39 8 383 0.12 1.15 2.30 0.45 1.37 -0.67 -0.16
1 1 40 5 9 0.07 -1.24 -0.97 -1.19 -1.11 -0.67 1.57
1 1 41 11 419 0.06 1.41 -0.89 2.29 2.79 0.43 -0.82
1 1 42 8 242 0.14 -0.81 -0.08 0.30 -0.05 0.43 -0.65
1 1 43 13 179 0.09 0.41 0.68 -0.76 -0.76 -0.67 0.40
1 1 44 5 375 0.04 0.06 -0.08 1.70 1.37 0.43 -0.79
1 1 45 20 129 0.14 -1.15 0.68 -0.79 -0.76 -0.67 -0.40
1 1 46 10 292 0.22 0.86 0.68 -0.65 -0.12 0.43 -1.41
1 1 47 5 79 0.12 -0.89 -1.04 -0.94 -0.05 -0.67 1.02
1 1 48 23 246 0.11 -0.42 0.68 0.46 -0.05 -0.67 -0.63
1 1 49 8 207 0.25 0.74 -0.89 -0.40 -0.40 0.43 0.52
1 1 50 11 27 0.06 -1.06 -1.27 -1.19 -1.11 -0.67 0.43
1 1 51 8 51 0.11 -1.23 -0.08 -1.05 -0.85 -0.67 0.94
1 1 52 19 288 0.09 0.81 -0.89 0.45 1.37 -0.67 0.88
1 1 53 7 154 0.1 -0.62 0.68 -0.15 -0.76 -0.67 0.84
1 1 54 10 261 0.15 0.61 -0.08 -0.67 -0.05 0.43 -1.40
1 1 55 10 195 0.15 0.18 0.77 -0.09 -0.76 -0.67 0.83
1 1 56 14 250 0.09 0.52 0.68 -0.69 -0.05 -0.67 -1.61
1 1 57 20 331 0.2 -0.63 0.68 0.30 -0.76 2.64 -0.95
1 1 58 9 379 0.15 1.33 -0.08 -0.65 -0.29 2.64 -1.52
1 1 59 14 11 0.21 -0.28 -1.05 -0.79 -0.76 2.64 0.53
1 1 60 29 359 0.13 1.36 0.68 0.18 1.37 0.43 0.77
1 1 61 6 337 0.1 2.46 0.68 0.21 -0.05 -0.67 -0.87
1 1 62 6 1 0.17 -0.17 -1.21 -1.02 -0.76 2.64 1.32
1 1 63 28 243 0.33 -0.33 2.30 -0.23 -0.46 -0.67 -0.88
1 1 64 8 274 0.07 0.41 -1.27 0.45 1.37 -0.67 0.68
1 1 65 13 362 0.14 1.07 0.75 0.35 1.37 0.43 1.34
1 1 66 10 143 0.07 -0.34 -0.89 -0.80 -0.05 -0.67 -1.66
1 1 67 4 265 0.05 -0.55 0.68 1.23 -0.05 -0.67 -0.69
1 1 68 11 13 0.15 -0.83 -0.89 -0.25 -0.76 2.64 -0.33
1 1 69 8 298 0.17 -0.62 0.20 2.29 -0.05 -0.67 -0.95
1 1 70 4 335 0.06 1.34 -0.08 0.45 1.37 -0.67 -0.08
1 1 71 20 204 0.16 0.09 -0.08 0.02 -0.05 -0.67 0.86
1 1 72 10 42 0.06 -1.49 -0.89 -0.75 -0.76 -0.67 1.04
1 1 73 1 429 0 3.08 0.68 0.04 4.20 0.43 0.71
1 1 74 14 186 0.14 -0.79 -0.89 0.45 -0.05 -0.67 -0.68
1 1 75 4 410 0.37 2.27 0.68 3.73 -0.23 -0.40 0.68
1 1 76 9 163 0.16 1.05 -0.89 -0.41 -0.60 -0.67 0.61
1 1 77 10 400 0.07 -0.03 0.68 1.70 1.37 0.43 -2.38
1 1 78 6 275 0.18 1.14 0.68 0.13 -0.05 -0.67 -0.18
1 1 79 25 241 0.16 -0.88 0.68 0.40 -0.05 -0.67 -1.06
1 1 80 6 245 0.14 -1.22 0.68 -0.30 -0.05 0.43 -0.91
1 1 81 21 120 0.16 -0.46 -0.08 -0.82 -0.62 -0.67 0.70
1 1 82 11 40 0.18 -0.93 -0.99 -1.19 -1.11 0.43 0.37
1 1 83 9 342 0.28 1.16 0.43 -0.52 -0.68 2.64 1.12
1 1 84 8 286 0.05 -0.72 1.11 0.50 -0.05 0.43 -0.83
1 1 85 8 33 0.1 -1.06 -0.89 -1.18 -1.02 -0.67 -0.99
1 1 86 5 282 0.23 -1.50 0.53 0.19 -0.48 0.43 -2.16
1 1 87 17 137 0.07 -0.31 0.68 -0.78 -0.76 -0.67 0.96
1 1 88 19 168 0.07 -0.08 -0.89 0.05 -0.05 -0.67 1.04
1 1 89 7 291 0.05 1.10 -0.89 0.15 1.37 -0.67 0.36
1 1 90 6 24 0.19 -0.97 -1.02 -1.07 -0.94 0.43 -1.40
1 1 91 4 434 0.59 4.07 1.49 1.29 0.30 2.64 0.07
1 1 92 19 409 0.65 0.92 0.42 1.41 1.37 2.64 -0.60
1 1 93 9 393 0.46 2.04 2.30 0.91 -0.05 -0.31 -0.34
1 1 94 8 22 0.08 -1.66 -1.27 -0.84 -0.76 -0.67 0.84
1 1 95 23 158 0.22 -1.41 0.68 -0.20 -0.70 -0.67 -1.05
1 1 96 11 330 0.22 1.55 0.68 -0.45 -0.31 0.43 -1.59
1 1 97 6 145 0.17 0.49 -0.89 -0.64 -0.76 -0.67 -0.17
1 1 98 12 121 0.15 0.21 -0.89 -0.80 -0.76 -0.67 -1.70
1 1 99 14 329 0.24 2.06 0.63 0.31 -0.25 0.43 0.99
1 1 100 16 299 0.05 1.21 -0.89 0.46 1.37 -0.67 0.86
1 1 101 5 328 0.1 -0.87 1.11 1.33 -0.05 0.43 -1.13
1 1 102 10 278 0.1 0.33 -0.93 0.45 1.37 -0.67 0.02
1 1 103 5 102 0.1 -1.05 0.68 -0.76 -0.76 -0.67 1.27
1 1 104 12 25 0.08 -1.25 -1.05 -0.78 -0.76 -0.67 1.57
1 1 105 9 385 0.25 2.05 0.34 -0.21 -0.05 2.64 1.12
1 1 106 10 231 0.18 -0.02 -0.08 0.02 -0.05 0.43 1.29
1 1 107 5 193 0.14 -0.66 -0.08 -0.33 -0.05 -0.67 -1.01
1 1 108 4 418 0.06 -0.03 0.68 3.07 1.37 0.43 -2.25
1 1 109 4 306 0.16 1.83 0.68 -0.59 -0.05 -0.67 -1.57
1 1 110 5 378 0.15 1.09 0.68 1.20 1.37 0.43 -0.11
1 1 111 2 308 0.07 -0.55 0.68 0.26 1.37 -0.67 -1.25
1 1 112 18 239 0.15 0.44 0.75 0.08 -0.05 -0.67 1.05
1 1 113 11 62 0.06 -1.14 -0.89 -0.81 -0.76 -0.67 0.73
1 1 114 5 169 0.07 -0.26 -0.89 0.47 -0.05 -0.67 1.40
1 1 115 18 415 0.11 0.74 -0.08 2.29 2.79 0.43 -0.93
1 1 116 5 97 0.13 0.23 -1.19 -1.05 -0.76 -0.67 0.77
1 1 117 24 19 0.22 -0.06 2.30 -0.89 -0.89 -0.67 1.18
1 1 118 9 184 0.17 -0.98 0.34 -0.29 -0.05 -0.67 -0.08
1 1 119 11 43 0.12 -0.82 -0.89 -1.04 -0.79 -0.67 -1.65
1 1 120 9 257 0.29 2.17 -0.62 0.10 -0.05 -0.55 0.65
1 1 121 27 155 0.18 0.15 0.68 -0.84 -0.76 -0.67 0.81
1 1 122 20 215 0.11 0.33 -0.08 -0.69 -0.05 -0.67 -1.64
1 1 123 14 348 0.24 0.61 0.74 0.37 1.37 0.43 0.25
1 1 124 13 162 0.12 0.01 -1.01 -0.67 -0.05 -0.67 -1.57
1 1 125 7 366 0.22 1.62 0.35 -0.29 1.37 -0.67 -1.65
1 1 126 9 77 0.02 -0.88 -0.89 -0.78 -0.76 -0.67 0.66
1 1 127 25 253 0.14 0.70 0.68 0.16 -0.05 -0.67 0.61
1 1 128 9 84 0.09 -0.27 -1.27 -0.81 -0.76 -0.67 0.81
1 1 129 3 398 0.04 -0.03 -0.08 2.29 1.37 0.43 -1.98
1 1 130 9 412 0.05 0.90 -0.89 2.29 2.79 0.43 -0.48
1 1 131 8 309 0.06 1.43 -0.89 0.41 1.37 -0.67 0.46
1 1 132 8 267 0.08 0.10 0.68 0.37 -0.05 0.43 1.57
1 1 133 16 252 0.22 0.94 -0.08 -0.40 -0.14 0.43 0.43
1 1 134 15 119 0.13 -0.60 -0.99 -0.75 -0.76 0.43 0.24
1 1 135 13 48 0.09 -0.66 -0.92 -1.19 -1.11 -0.67 0.82
1 1 136 9 326 0.11 1.45 -0.08 0.32 1.37 -0.67 0.38
1 1 137 11 386 0.22 1.37 0.68 -0.66 -0.18 2.64 -1.36
1 1 138 20 255 0.15 0.43 -0.89 -0.34 -0.05 2.64 0.68
1 1 139 8 161 0.14 -0.68 -0.94 -0.08 -0.05 0.43 1.41
1 1 140 10 38 0.13 -1.22 -1.19 -0.92 -0.76 0.43 0.91
1 1 141 14 180 0.12 0.09 0.68 -0.56 -0.76 -0.67 0.07
1 1 142 13 427 0.21 2.01 0.62 2.29 2.79 0.43 -0.18
1 1 143 15 354 0.13 1.63 0.68 0.39 1.37 -0.67 0.26
1 1 144 11 301 0.14 0.82 -1.03 0.15 1.37 -0.67 -0.85
1 1 145 7 205 0.13 0.24 -0.08 -0.05 -0.05 -0.67 1.57
1 1 146 10 327 0.14 0.66 0.68 0.60 1.37 -0.67 0.42
1 1 147 11 403 0.11 0.92 2.30 1.22 1.37 0.43 -0.79
1 1 148 7 127 0.08 -0.20 -0.89 -0.10 -0.76 -0.67 0.69
1 1 149 6 217 0.11 0.41 -0.89 0.26 -0.05 -0.67 -0.34
1 1 150 11 323 0.1 0.96 -0.89 0.46 1.37 0.43 0.72
1 1 151 9 208 0.16 0.16 0.68 -0.60 -0.05 -0.67 0.43
1 1 152 14 405 0.14 -0.04 0.68 2.29 1.37 0.43 -2.24
1 1 153 10 98 0.08 -0.22 -0.89 -1.14 -0.76 -0.67 0.33
1 1 154 7 47 0.05 -0.99 -0.89 -1.16 -0.76 -0.67 1.03
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1 1 412 6 426 0.2 3.36 0.68 -0.27 1.37 2.64 -0.22
1 1 413 12 285 0.1 0.72 -1.24 0.30 1.37 -0.67 0.32
1 1 414 8 363 0.08 1.28 1.11 0.45 1.37 -0.67 1.36
1 1 415 8 437 0.27 1.02 1.00 3.07 2.79 2.64 -2.30
1 1 416 7 284 0.19 0.20 -0.66 -0.74 -0.05 2.64 -0.71
1 1 417 9 264 0.06 0.29 -0.89 0.45 1.37 -0.67 0.66
1 1 418 21 238 0.21 0.24 -0.08 -0.09 -0.05 0.43 0.69
1 1 419 3 296 0.02 -0.47 0.68 0.03 -0.05 0.43 -2.34
1 1 420 10 100 0.16 -0.44 -0.97 -0.87 -0.76 0.43 1.21
1 1 421 11 174 0.15 -0.61 0.68 -0.02 -0.76 -0.67 0.17
1 1 422 9 311 0.25 1.52 -0.53 -0.55 -0.76 2.64 0.36
1 1 423 6 135 0.09 -0.58 -1.27 0.12 -0.05 -0.67 1.29
1 1 424 5 368 0.15 2.37 0.68 0.36 1.37 -0.67 0.68
1 1 425 9 373 0.12 1.65 0.68 0.39 1.37 0.43 -0.01
1 1 426 10 228 0.13 0.42 -0.08 -0.33 -0.05 -0.67 -0.92
1 1 427 20 86 0.22 -1.23 -0.93 -0.85 -0.83 0.43 -0.46
1 1 428 7 106 0.06 -0.07 -0.89 -0.76 -0.76 -0.67 0.98
1 1 429 8 138 0.12 -0.45 -0.99 -0.78 -0.76 0.43 -0.77
1 1 430 8 30 0.12 -0.51 1.05 -1.19 -1.11 -0.67 1.36
1 1 431 19 357 0.16 1.03 0.68 -0.27 -0.05 2.64 0.61
1 1 432 20 406 0.38 0.02 2.30 0.99 -0.05 2.64 -1.12
1 1 433 10 302 0.26 1.83 0.53 -0.09 -0.33 0.43 0.24
1 1 434 5 73 0.04 -0.72 -0.89 -0.95 -0.76 -0.67 0.82
1 1 435 1 440 0 5.51 0.68 3.07 4.20 2.64 0.50
1 1 436 14 300 0.29 2.04 0.68 0.38 -0.15 -0.67 0.69
1 1 437 19 74 0.1 -1.10 -0.89 -0.81 -0.76 -0.67 -0.90
1 1 438 7 347 0.13 1.21 -0.08 0.41 1.37 0.43 0.59
1 1 439 31 374 0.28 -0.27 0.87 0.49 -0.05 2.64 -1.24
1 1 440 17 233 0.2 -0.48 0.68 -0.10 -0.13 0.43 0.60

Now let us understand what each column in the above table means:

All the columns after this will contain centroids for each cell. They can also be called a codebook, which represents a collection of all centroids or codewords.

Now, let’s check the compression summary for HVT (map A) where n_cell was set to 440. The table below shows no of cells, no of cells having quantization error below threshold and percentage of cells having quantization error below threshold for each level.

mapA_compression_summary <- map_A[[3]]$compression_summary %>%  dplyr::mutate_if(is.numeric, funs(round(.,4)))
compressionSummaryTable(mapA_compression_summary)
segmentLevel noOfCells noOfCellsBelowQuantizationError percentOfCellsBelowQuantizationErrorThreshold parameters
1 440 355 0.81 n_cells: 440 quant.err: 0.2 distance_metric: L1_Norm error_metric: max quant_method: kmeans

As it can be seen from the table above, 81% of the cells have hit the quantization threshold error.Since we are successfully able to attain the desired compression percentage, so we will not further subdivide the cells

Now let’s try to understand plotHVT function. The parameters have been explained in detail below:

plotHVT(hvt.results, line.width, color.vec, pch1 = 21, centroid.size = 3, title = NULL, maxDepth = 1)

Let’s plot the Voronoi tessellation for layer 1 (map A).

muHVT::plotHVT(map_A,
        line.width = c(0.4), 
        color.vec = c("#141B41"),
        centroid.size = 0.01,
        maxDepth = 1) 
Figure 2: The Voronoi Tessellation for layer 1 (map A) shown for the 440 cells in the dataset ’computers’

Figure 2: The Voronoi Tessellation for layer 1 (map A) shown for the 440 cells in the dataset ’computers’

Heat Maps

We will now overlay all the features as heatmap over the Voronoi Tessellation plot for better visualization and identification of patterns, trends, and variations in the data.

Let’s have a look at the function hvtHmap that we will use to overlay features as heatmap.

hvtHmap(hvt.results, dataset, child.level, hmap.cols, color.vec ,line.width, palette.color = 6)

Now let’s plot the Voronoi Tessellation with the heatmap overlaid for all the features in the torus data for better visualization and interpretation of data patterns and distributions.

The heatmaps displayed below provides a visual representation of the spatial characteristics of the computers data, allowing us to observe patterns and trends in the distribution of each of the features (n,price,speed,hd,ram,screen,ads). The sheer green shades highlight regions with higher values in each of the heatmaps, while the indigo shades indicate areas with the lowest values in each of the heatmaps. By analyzing these heatmaps, we can gain insights into the variations and relationships between each of these features within the computers data.


  hvtHmap(
  map_A,
  trainComputers,
  child.level = 1,
  hmap.cols = "n",
  line.width = c(0.2),
  color.vec = c("#141B41"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = T,
  quant.error.hmap = 0.2,
  n_cells.hmap = 440,
) 
Figure 3: The Voronoi Tessellation with the heat map overlaid for No. of entities in each cell

Figure 3: The Voronoi Tessellation with the heat map overlaid for No. of entities in each cell


  hvtHmap(
  map_A,
  trainComputers,
  child.level = 1,
  hmap.cols = "price",
  line.width = c(0.2),
  color.vec = c("#141B41"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = T,
  quant.error.hmap = 0.2,
  n_cells.hmap = 440,
) 
Figure 4: The Voronoi Tessellation with the heat map overlaid for variable ’price’ in the ’computers’ dataset

Figure 4: The Voronoi Tessellation with the heat map overlaid for variable ’price’ in the ’computers’ dataset


  hvtHmap(
  map_A,
  trainComputers,
  child.level = 1,
  hmap.cols = "speed",
  line.width = c(0.2),
  color.vec = c("#141B41"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = T,
  quant.error.hmap = 0.2,
  n_cells.hmap = 440,
) 
Figure 5: The Voronoi Tessellation with the heat map overlaid for variable ’speed’ in the ’computers’ dataset

Figure 5: The Voronoi Tessellation with the heat map overlaid for variable ’speed’ in the ’computers’ dataset


  hvtHmap(
  map_A,
  trainComputers,
  child.level = 1,
  hmap.cols = "hd",
  line.width = c(0.2),
  color.vec = c("#141B41"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = T,
  quant.error.hmap = 0.2,
  n_cells.hmap = 440,
) 
Figure 6: The Voronoi Tessellation with the heat map overlaid for variable ’hd’ in the ’computers’ dataset

Figure 6: The Voronoi Tessellation with the heat map overlaid for variable ’hd’ in the ’computers’ dataset


  hvtHmap(
  map_A,
  trainComputers,
  child.level = 1,
  hmap.cols = "ram",
  line.width = c(0.2),
  color.vec = c("#141B41"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = T,
  quant.error.hmap = 0.2,
  n_cells.hmap = 440,
) 
Figure 7: The Voronoi Tessellation with the heat map overlaid for variable ’ram’ in the ’computers’ dataset

Figure 7: The Voronoi Tessellation with the heat map overlaid for variable ’ram’ in the ’computers’ dataset


  hvtHmap(
  map_A,
  trainComputers,
  child.level = 1,
  hmap.cols = "screen",
  line.width = c(0.2),
  color.vec = c("#141B41"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = T,
  quant.error.hmap = 0.2,
  n_cells.hmap = 440,
) 
Figure 8: The Voronoi Tessellation with the heat map overlaid for variable ’screen’ in the ’computers’ dataset

Figure 8: The Voronoi Tessellation with the heat map overlaid for variable ’screen’ in the ’computers’ dataset


  hvtHmap(
  map_A,
  trainComputers,
  child.level = 1,
  hmap.cols = "ads",
  line.width = c(0.2),
  color.vec = c("#141B41"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = T,
  quant.error.hmap = 0.2,
  n_cells.hmap = 440,
) 
Figure 9: The Voronoi Tessellation with the heat map overlaid for variable ’ads’ in the ’computers’ dataset

Figure 9: The Voronoi Tessellation with the heat map overlaid for variable ’ads’ in the ’computers’ dataset

4 Map B : Compressed Novelty Map

Let us try to visualize the Map B from the flow diagram below.

Figure 10: Flow map with highlighted bounding box in red around map B

Figure 10: Flow map with highlighted bounding box in red around map B

In this section, we will manually figure out the novelty cells from the plotted map A and store it in identified_Novelty_cells variable.

Note: For manual selecting the novelty cells from map A, one can enhance its interactivity by adding plotly elements to the code. This will transform map A into an interactive plot, allowing users to actively engage with the data. By hovering over the centroids of the cells, a tag containing segment child information will be displayed. Users can explore the map by hovering over different cells and selectively choose the novelty cells they wish to consider. Added an image for reference.

Figure 11: Manually selecting novelty cells

Figure 11: Manually selecting novelty cells

The removeNovelty function removes the identified novelty cell(s) from the training dataset (containing 5007 datapoints) and stores those records separately.

It takes input as the cell number (Segment.Child) of the manually identified novelty cell(s) and the compressed HVT map (map A) with 440 cells. It returns a list of two items: dataset with novelty records, and a subset of the dataset without the novelty records.

identified_Novelty_cells <<- c(73,321,332,338,435)   #73,321,332,338,435
output_list <- removeNovelty(identified_Novelty_cells, map_A)

[1] “The following cell(s) have been removed as novelties from the dataset: 73 321 332 338 435”

data_with_novelty <- output_list[[1]]
dataset_without_novelty <- output_list[[2]]

Let’s have a look at the data with novelties(containing 24 records). For the sake of brevity, we will only show the first 10 rows.

novelty_data <- data_with_novelty
novelty_data$Row.No <- row.names(novelty_data)
novelty_data <- novelty_data %>% dplyr::select("Row.No","Cell.ID","Cell.Number","price","speed","hd","ram","screen","ads")
colnames(novelty_data) <- c("Row.No","Cell.ID","Segment.Child","price","speed","hd","ram","screen","ads")
novelty_data %>% head(100) %>% 
  as.data.frame() %>%
  Table(scroll = T, limit = 20)
Row.No Cell.ID Segment.Child price speed hd ram screen ads
1 429 73 3.0762240 0.6794579 0.0421969 4.2031619 0.4307274 0.7120258
2 438 321 2.6449847 0.6794579 6.5710368 1.3676416 0.4307274 0.6851382
3 438 321 1.6578103 2.2969425 6.5710368 1.3676416 0.4307274 -1.2507722
4 439 332 0.9130997 0.6794579 4.6232922 2.7854017 0.4307274 -2.4607161
5 439 332 1.8569770 1.1076156 4.6232922 4.2031619 2.6404120 -2.4607161
6 439 332 1.5192595 2.2969425 4.6232922 4.2031619 0.4307274 -2.4607161
7 439 332 1.4482522 1.1076156 4.6232922 4.2031619 0.4307274 -2.4607161
8 439 332 1.8569770 1.1076156 4.6232922 4.2031619 2.6404120 -2.4607161
9 439 332 1.1555636 2.2969425 4.6232922 2.7854017 0.4307274 -2.4607161
10 439 332 1.7773103 1.1076156 4.6232922 4.2031619 0.4307274 -2.4607161
11 439 332 1.3460710 0.6794579 4.6232922 4.2031619 0.4307274 -2.4607161
12 439 332 1.4482522 1.1076156 4.6232922 4.2031619 0.4307274 -2.4607161
13 218 338 -1.4959522 0.6794579 0.4473277 -0.7589986 -0.6741149 -2.2993903
14 218 338 -1.5115391 0.6794579 0.4473277 -0.7589986 -0.6741149 -1.9767386
15 218 338 -1.1668940 0.6794579 0.4473277 -0.7589986 -0.6741149 -2.2859465
16 218 338 -1.4959522 0.6794579 0.4473277 -0.7589986 -0.6741149 -2.4472723
17 218 338 -1.5981334 0.6794579 0.4473277 -0.7589986 -0.6741149 -2.2859465
18 218 338 -1.1668940 0.6794579 0.4473277 -0.7589986 -0.6741149 -2.2993903
19 218 338 -1.1668940 0.6794579 0.4473277 -0.7589986 -0.6741149 -2.4472723
20 218 338 -1.3227637 0.6794579 0.4473277 -0.7589986 -0.6741149 -1.9767386

4.1 Voronoi Tessellation with highlighted novelty cell

The plotCells function is used to plot the Voronoi tessellation using the compressed HVT map (map A) containing 440 cells and highlights the identified novelty cell(s) i.e 5 cells (containing 24 records) in red on the map.

plotCells(identified_Novelty_cells, map_A,line.width = c(0.4),centroid.size = 0.01)
Figure 12: The Voronoi Tessellation constructed using the compressed HVT map (map A) with the novelty cell(s) highlighted in red

Figure 12: The Voronoi Tessellation constructed using the compressed HVT map (map A) with the novelty cell(s) highlighted in red

We pass the dataframe with novelty records (24 records) to HVT function along with other model parameters mentioned below to generate map B (layer2)

Model Parameters

colnames(data_with_novelty) <- c("Cell.ID","Segment.Child","price","speed","hd","ram","screen","ads")
dataset_with_novelty <- data_with_novelty[,-1:-2]
map_B <- list()
mapA_scale_summary = map_A[[3]]$scale_summary
map_B <- muHVT::HVT(dataset_with_novelty,
                  n_cells = 12 ,   #6
                  depth = 1,
                  quant.err = 0.2,
                  projection.scale = 10,
                  normalize = F,
                  distance_metric = "L1_Norm",
                  error_metric = "max",
                  quant_method = "kmeans",
                  diagnose = F
                  )

The datatable displayed below is the summary from map B (layer 2) showing Cell.ID, Centroids and Quantization Error for each of the 12 cells.

summaryTable(map_B[[3]]$summary,scroll = T,limit = 500)
Segment.Level Segment.Parent Segment.Child n Cell.ID Quant.Error price speed hd ram screen ads
1 1 1 1 6 0 -1.08 0.68 0.45 -0.76 -0.67 -1.98
1 1 2 1 3 0 -1.51 0.68 0.45 -0.76 -0.67 -1.98
1 1 3 2 1 0.01 -1.55 -0.08 0.45 -0.76 -0.67 -1.98
1 1 4 2 11 0 1.86 1.11 4.62 4.20 2.64 -2.46
1 1 5 1 7 0 3.08 0.68 0.04 4.20 0.43 0.71
1 1 6 5 8 0.31 1.39 0.94 4.62 3.92 0.43 -2.46
1 1 7 1 12 0 5.51 0.68 3.07 4.20 2.64 0.50
1 1 8 2 9 0.15 1.34 2.30 4.62 3.49 0.43 -2.46
1 1 9 1 4 0 -1.32 0.68 0.45 -0.76 -0.67 -1.98
1 1 10 3 2 0.02 -1.53 0.68 0.45 -0.76 -0.67 -2.34
1 1 11 2 10 0.38 2.15 1.49 6.57 1.37 0.43 -0.28
1 1 12 3 5 0.02 -1.17 0.68 0.45 -0.76 -0.67 -2.34

Now let’s check the compression summary for HVT (map B). The table below shows no of cells, no of cells having quantization error below threshold and percentage of cells having quantization error below threshold for each level.

mapB_compression_summary <- map_B[[3]]$compression_summary %>%  dplyr::mutate_if(is.numeric, funs(round(.,4)))
compressionSummaryTable(mapB_compression_summary)
segmentLevel noOfCells noOfCellsBelowQuantizationError percentOfCellsBelowQuantizationErrorThreshold parameters
1 12 10 0.83 n_cells: 12 quant.err: 0.2 distance_metric: L1_Norm error_metric: max quant_method: kmeans

As it can be seen from the table above, 83% of the cells have hit the quantization threshold error.Since we are successfully able to attain the desired compression percentage, so we will not further subdivide the cells

5 Map C : Compressed Map without Novelty

Let us try to visualize the compressed Map C from the flow diagram below.

Figure 13:Flow map with highlighted bounding box in red around compressed map C

Figure 13:Flow map with highlighted bounding box in red around compressed map C

5.0.1 Iteration 1:

With the Novelties removed, we construct another hierarchical Voronoi tessellation map C layer 2 on the dataset without Novelty (containing 4986 records) and below mentioned model parameters.

Model Parameters

map_C <- list()
mapA_scale_summary = map_A[[3]]$scale_summary
map_C <- muHVT::HVT(dataset_without_novelty,
                  n_cells = 10,
                  depth = 2,
                  quant.err = 0.2,
                  projection.scale = 10,
                  normalize = F,
                  distance_metric = "L1_Norm",
                  error_metric = "max",
                  quant_method = "kmeans",
                  diagnose = F,
                  scale_summary = mapA_scale_summary)

Now let’s check the compression summary for HVT (map C) where n_cell was set to 10. The table below shows no of cells, no of cells having quantization error below threshold and percentage of cells having quantization error below threshold for each level.

mapC_compression_summary <- map_C[[3]]$compression_summary %>%  dplyr::mutate_if(is.numeric, funs(round(.,4)))
compressionSummaryTable(mapC_compression_summary)
segmentLevel noOfCells noOfCellsBelowQuantizationError percentOfCellsBelowQuantizationErrorThreshold parameters
1 10 0 0 n_cells: 10 quant.err: 0.2 distance_metric: L1_Norm error_metric: max quant_method: kmeans
2 100 7 0.07 n_cells: 10 quant.err: 0.2 distance_metric: L1_Norm error_metric: max quant_method: kmeans

As it can be seen from the table above, 0% of the cells have hit the quantization threshold error in level 1 and 7% of the cells have hit the quantization threshold error in level 2

5.0.2 Iteration 2:

Since, we are yet to achive atleast 80% compression at depth 2. Let’s try to compress again using the below mentioned set of model parameters and the dataset without novelty (containing 4983 records).

Model Parameters

map_C <- list()
map_C <- muHVT::HVT(dataset_without_novelty,
                  n_cells = 23,    #23
                  depth = 2,
                  quant.err = 0.2,
                  projection.scale = 10,
                  normalize = F,
                  distance_metric = "L1_Norm",
                  error_metric = "max",
                  quant_method = "kmeans",
                  diagnose = F,
                  scale_summary = mapA_scale_summary)

The datatable displayed below is the summary from map C (layer2). showing Cell.ID, Centroids and Quantization Error for each of the 531 cells.

summaryTable(map_C[[3]]$summary,scroll = T,limit = 500)
Segment.Level Segment.Parent Segment.Child n Cell.ID Quant.Error price speed hd ram screen ads
1 1 1 391 512 0.56 -1.27 -1.04 -0.91 -0.83 -0.59 0.86
1 1 2 105 96 1.02 2.08 0.75 0.11 0.71 2.64 0.56
1 1 3 190 55 1.37 1.48 0.02 2.32 2.63 0.12 -0.22
1 1 4 86 15 0.94 0.87 1.27 2.61 2.57 1.33 -1.76
1 1 5 257 326 0.49 0.41 0.45 -0.08 -0.20 -0.67 0.66
1 1 6 116 201 0.77 1.57 0.45 -0.24 0.27 -0.30 -1.30
1 1 7 235 228 0.58 0.85 -0.82 0.42 1.37 -0.47 0.52
1 1 8 149 185 0.84 -0.79 1.73 0.76 -0.22 -0.28 -1.75
1 1 9 353 306 0.69 -0.77 0.55 0.28 -0.22 -0.17 -0.79
1 1 10 234 297 0.54 0.25 0.50 -0.11 -0.16 0.43 0.66
1 1 11 330 478 0.56 -1.18 -0.79 -0.70 -0.76 -0.52 -0.69
1 1 12 373 434 0.6 -0.50 0.40 -0.84 -0.84 -0.56 0.66
1 1 13 209 147 0.81 1.32 0.99 0.36 1.37 -0.01 0.70
1 1 14 337 471 0.36 -0.51 -0.97 -0.87 -0.75 -0.67 0.57
1 1 15 283 404 0.71 0.06 -0.40 -0.78 -0.40 -0.42 -1.42
1 1 16 168 142 0.85 0.13 0.66 0.48 -0.02 2.64 -0.97
1 1 17 285 384 0.53 -0.04 -0.96 0.05 -0.12 -0.65 0.54
1 1 18 118 301 0.75 0.35 2.30 -0.13 -0.29 -0.28 0.82
1 1 19 256 414 0.47 -0.47 -0.84 -0.43 -0.48 0.43 0.60
1 1 20 78 57 1 0.18 1.67 2.05 1.31 0.39 -1.97
1 1 21 171 360 0.64 0.24 -0.46 -0.37 -0.41 2.64 0.59
1 1 22 170 130 1.28 0.28 -0.01 1.64 0.99 0.21 -0.62
1 1 23 89 219 0.88 1.98 0.59 0.20 -0.20 0.12 0.58
2 1 1 19 528 0.09 -1.31 -1.17 -1.19 -1.11 -0.67 0.99
2 1 2 18 479 0.31 -1.42 -0.87 -0.21 -0.72 -0.67 0.53
2 1 3 28 521 0.1 -1.47 -1.22 -1.11 -0.76 -0.67 0.89
2 1 4 10 530 0.14 -1.84 -1.04 -1.20 -1.11 -0.67 0.79
2 1 5 27 519 0.1 -1.20 -1.09 -1.19 -1.11 -0.67 0.50
2 1 6 13 524 0.18 -1.36 -1.10 -0.99 -0.87 0.43 1.36
2 1 7 5 523 0.04 -1.19 -1.27 -0.78 -0.76 -0.67 1.57
2 1 8 23 494 0.06 -1.18 -0.89 -0.78 -0.76 -0.67 0.72
2 1 9 27 514 0.14 -1.35 -1.27 -1.08 -0.76 -0.67 0.39
2 1 10 35 510 0.1 -1.08 -1.27 -0.88 -0.76 -0.67 0.90
2 1 11 6 529 0.15 -1.22 -0.62 -1.19 -1.11 -0.67 1.50
2 1 12 10 513 0.07 -0.95 -0.89 -0.85 -0.76 -0.67 1.57
2 1 13 10 517 0.22 -1.70 -1.19 -0.73 -0.83 -0.67 0.57
2 1 14 11 472 0.17 -1.19 -1.13 -0.33 -0.05 -0.67 0.97
2 1 15 11 507 0.19 -1.00 -0.93 -1.17 -0.63 -0.67 0.97
2 1 16 7 531 0.07 -1.58 -1.27 -1.18 -0.96 -0.67 1.57
2 1 17 26 499 0.09 -1.31 -0.89 -0.92 -0.76 -0.67 0.36
2 1 18 23 515 0.07 -0.99 -0.89 -1.19 -1.11 -0.67 0.92
2 1 19 13 520 0.14 -1.56 -0.98 -0.74 -0.76 -0.67 1.34
2 1 20 15 489 0.12 -1.05 -0.89 -0.26 -0.76 -0.67 1.31
2 1 21 16 503 0.18 -1.48 -0.79 -0.73 -0.76 -0.67 0.76
2 1 22 15 518 0.26 -1.37 -1.07 -1.09 -1.07 0.43 0.66
2 1 23 23 500 0.07 -1.03 -0.89 -0.82 -0.76 -0.67 1.06
2 2 1 4 108 0.12 2.31 0.68 -0.12 -0.05 2.64 1.31
2 2 2 3 118 0.11 2.53 0.68 -0.47 -0.76 2.64 0.36
2 2 3 7 99 0.21 1.06 0.80 0.29 1.37 2.64 0.35
2 2 4 2 89 0.06 1.09 2.30 0.25 -0.05 2.64 1.57
2 2 5 7 59 0.13 3.21 0.68 -0.27 1.37 2.64 0.53
2 2 6 7 88 0.11 1.85 0.68 0.16 1.37 2.64 0.85
2 2 7 2 145 0.11 1.14 0.68 0.10 -0.05 2.64 1.36
2 2 8 3 38 0.11 3.32 0.68 -0.27 1.37 2.64 -0.78
2 2 9 6 100 0.17 2.86 0.68 0.10 -0.05 2.64 0.48
2 2 10 2 24 0.11 3.50 2.30 1.23 -0.05 2.64 -0.23
2 2 11 2 12 0.38 4.64 0.68 1.36 0.66 2.64 0.37
2 2 12 6 56 0.25 1.52 2.30 0.32 1.37 2.64 0.77
2 2 13 4 50 0.34 1.64 0.49 1.90 1.37 2.64 0.14
2 2 14 13 76 0.22 2.42 0.68 0.03 1.37 2.64 0.53
2 2 15 4 103 0.12 1.08 2.30 0.14 -0.05 2.64 0.52
2 2 16 11 167 0.13 1.23 0.68 -0.20 -0.05 2.64 0.59
2 2 17 1 107 0 1.99 -0.08 0.49 -0.05 2.64 -0.62
2 2 18 4 84 0.15 1.52 0.68 0.34 1.37 2.64 1.36
2 2 19 5 169 0.17 1.81 -0.08 -0.29 -0.19 2.64 0.99
2 2 20 4 70 0.11 2.69 -0.89 -0.27 1.37 2.64 0.69
2 2 21 4 122 0.11 1.99 0.68 0.22 -0.05 2.64 0.57
2 2 22 3 60 0.12 2.74 -0.89 -0.27 1.37 2.64 -0.78
2 2 23 1 195 0 1.63 0.68 -0.95 -0.76 2.64 0.69
2 3 1 5 39 0.04 1.54 -0.08 2.29 2.79 0.43 -0.81
2 3 2 3 9 0.05 1.71 -0.89 2.29 2.79 2.64 -0.55
2 3 3 10 51 0.07 1.10 -0.08 2.29 2.79 0.43 -0.56
2 3 4 5 32 0.39 3.74 -0.10 2.60 1.37 -0.67 0.96
2 3 5 3 19 0.02 2.16 2.30 2.29 2.79 -0.67 0.04
2 3 6 1 20 0 2.03 2.30 2.29 2.79 0.43 0.35
2 3 7 16 49 0.18 1.49 -0.89 2.29 2.79 0.43 -0.06
2 3 8 7 40 0.09 1.80 -0.08 2.29 2.79 0.43 -0.26
2 3 9 2 54 0.05 2.90 0.68 3.73 -0.05 -0.67 0.69
2 3 10 1 91 0 1.16 0.68 2.29 1.37 -0.67 0.04
2 3 11 7 46 0.05 1.16 0.68 2.29 2.79 0.43 -0.49
2 3 12 4 77 0.12 1.66 0.68 2.44 1.37 0.43 0.80
2 3 13 7 37 0.08 1.63 0.68 2.29 2.79 0.43 -0.73
2 3 14 12 53 0.1 1.69 0.68 2.29 2.79 -0.67 0.38
2 3 15 2 43 0.04 3.07 0.68 2.29 1.37 -0.67 -0.87
2 3 16 5 23 0.04 2.06 2.30 2.29 2.79 -0.67 0.35
2 3 17 12 45 0.06 0.92 0.68 2.29 2.79 0.43 -0.86
2 3 18 5 82 0.13 1.35 0.68 2.47 1.37 0.43 0.11
2 3 19 5 17 0.04 2.23 2.30 2.29 2.79 -0.67 0.69
2 3 20 24 61 0.12 1.30 -0.89 2.29 2.79 -0.67 0.33
2 3 21 9 36 0.18 2.07 0.68 2.29 2.79 0.43 -0.03
2 3 22 13 52 0.11 0.65 -0.08 2.29 2.79 0.43 -1.03
2 3 23 32 48 0.13 1.15 -0.89 2.29 2.79 0.43 -0.66
2 4 1 5 7 0.11 0.51 2.30 2.05 1.37 2.64 -2.33
2 4 2 8 18 0.07 0.52 0.68 3.07 2.79 0.43 -2.36
2 4 3 6 41 0.05 0.79 0.68 2.29 2.79 0.43 -1.24
2 4 4 2 3 0 1.08 2.30 3.07 2.79 0.43 -2.46
2 4 5 3 8 0.13 1.91 0.43 2.29 2.79 2.64 -0.55
2 4 6 1 11 0 0.01 1.11 3.07 2.79 0.43 -2.45
2 4 7 3 26 0.03 0.73 -0.08 3.07 2.79 0.43 -1.98
2 4 8 1 4 0 0.99 -0.08 3.07 2.79 2.64 -1.98
2 4 9 3 2 0.05 1.48 2.30 2.29 2.79 2.64 -1.08
2 4 10 2 14 0.02 0.81 0.68 3.07 2.79 0.43 -2.46
2 4 11 1 6 0 0.74 2.30 3.07 2.79 0.43 -1.98
2 4 12 2 16 0.02 0.89 1.11 3.07 2.79 0.43 -1.98
2 4 13 2 29 0.04 0.84 2.30 1.70 1.37 2.64 -1.02
2 4 14 6 5 0.03 0.74 2.30 3.07 2.79 0.43 -2.40
2 4 15 7 1 0.23 1.03 1.16 3.07 2.79 2.64 -2.34
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2 4 17 6 22 0.25 0.85 -0.22 2.29 2.79 2.64 -0.97
2 4 18 2 13 0.05 1.21 0.68 2.29 2.79 2.64 -1.10
2 4 19 5 30 0.11 0.32 0.68 2.17 1.37 2.64 -2.29
2 4 20 6 10 0.04 0.69 1.11 3.07 2.79 0.43 -2.32
2 4 21 1 34 0 0.30 -0.08 2.29 1.37 2.64 -1.98
2 4 22 6 21 0.06 1.46 2.30 2.29 2.79 0.43 -1.01
2 4 23 3 28 0.01 1.00 2.30 2.29 2.79 0.43 -0.79
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2 5 5 6 311 0.06 -0.28 0.68 0.45 -0.05 -0.67 0.30
2 5 6 8 287 0.15 0.45 0.68 0.16 -0.05 -0.67 -0.20
2 5 7 5 305 0.06 -0.07 0.68 0.45 -0.05 -0.67 0.48
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2 5 12 7 314 0.16 1.02 0.68 -0.39 -0.15 -0.67 1.12
2 5 13 17 363 0.2 0.66 0.63 -0.69 -0.76 -0.67 0.15
2 5 14 15 278 0.11 1.06 0.68 0.06 -0.05 -0.67 0.76
2 5 15 8 356 0.16 0.13 0.79 -0.13 -0.76 -0.67 0.38
2 5 16 11 275 0.19 1.06 0.68 -0.09 -0.05 -0.67 0.19
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2 5 20 7 386 0.14 1.08 -0.08 -0.62 -0.76 -0.67 0.63
2 5 21 12 336 0.2 -0.17 0.68 -0.04 -0.05 -0.67 0.86
2 5 22 7 364 0.13 0.24 -0.08 -0.05 -0.05 -0.67 1.57
2 5 23 0 NA NA NA NA NA NA NA NA
2 6 1 6 184 0.1 2.46 0.68 0.21 -0.05 -0.67 -0.87
2 6 2 9 133 0.29 1.43 0.51 -0.44 1.37 0.43 -1.15
2 6 3 2 233 0.08 1.08 0.68 0.47 -0.05 -0.67 -0.71
2 6 4 9 247 0.22 0.90 0.59 -0.69 -0.13 0.43 -1.39
2 6 5 2 194 0.08 2.30 0.30 -0.32 -0.05 -0.67 -1.71
2 6 6 8 238 0.26 1.04 0.58 -0.29 -0.14 0.43 -0.77
2 6 7 9 127 0.06 2.98 0.68 0.28 -0.05 -0.67 -1.67
2 6 8 4 165 0.11 1.26 -0.08 -0.07 1.37 -0.67 -1.37
2 6 9 5 124 0.19 1.76 0.53 -0.29 1.37 -0.67 -1.66
2 6 10 1 101 0 3.77 0.68 0.15 -0.05 -0.67 -1.72
2 6 11 5 292 0.22 1.44 0.53 -0.77 -0.33 -0.67 -1.67
2 6 12 1 365 0 1.35 -0.08 -0.67 -0.76 -0.67 -0.62
2 6 13 4 149 0.06 1.43 0.68 0.15 1.37 -0.67 -0.87
2 6 14 10 197 0.2 1.57 0.68 -0.47 -0.33 0.43 -1.64
2 6 15 3 159 0.2 1.48 2.30 0.28 -0.05 -0.67 -0.87
2 6 16 3 280 0.1 0.85 -0.08 0.22 -0.05 -0.67 -0.68
2 6 17 9 191 0.15 1.09 -0.93 -0.29 1.37 -0.67 -1.62
2 6 18 4 140 0.08 3.03 -0.08 0.15 -0.05 -0.67 -1.65
2 6 19 7 294 0.05 0.73 0.68 -0.69 -0.05 -0.67 -1.60
2 6 20 3 112 0.09 2.96 0.68 0.12 -0.05 0.43 -1.72
2 6 21 2 270 0.04 1.61 0.68 -0.71 -0.05 -0.67 -0.87
2 6 22 8 279 0.09 0.84 0.68 -0.36 -0.05 -0.67 -0.84
2 6 23 2 237 0.08 2.30 -0.49 0.15 -0.05 -0.67 -1.12
2 7 1 8 210 0.16 0.51 -1.18 0.46 1.37 0.43 1.10
2 7 2 16 231 0.12 1.01 -0.91 0.35 1.37 -0.67 0.40
2 7 3 12 211 0.1 1.39 -0.89 0.37 1.37 -0.67 0.29
2 7 4 8 209 0.06 0.35 -0.89 1.20 1.37 -0.67 0.35
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2 7 6 12 202 0.18 0.49 -1.02 0.55 1.37 0.43 0.36
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2 7 10 20 220 0.09 1.20 -0.91 0.45 1.37 -0.67 0.84
2 7 11 9 265 0.07 0.48 -1.27 0.45 1.37 -0.67 0.66
2 7 12 14 190 0.21 1.09 -0.89 0.28 1.37 0.43 0.63
2 7 13 9 222 0.09 0.82 -1.06 0.45 1.37 -0.67 -0.07
2 7 14 7 168 0.2 0.97 -1.00 0.03 1.37 0.43 -0.83
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2 7 17 7 262 0.04 0.22 -0.89 0.45 1.37 -0.67 0.04
2 7 18 7 285 0.07 0.28 -1.22 0.45 1.37 -0.67 1.12
2 7 19 6 179 0.12 1.31 -0.08 0.35 1.37 -0.67 -0.26
2 7 20 17 189 0.14 1.26 -0.08 0.46 1.37 -0.67 0.84
2 7 21 3 316 0.02 0.10 -1.27 0.45 1.37 -0.67 1.57
2 7 22 11 183 0.11 1.44 -0.08 0.34 1.37 -0.67 0.42
2 7 23 11 251 0.09 0.72 -1.24 0.29 1.37 -0.67 0.36
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2 8 2 2 282 0 -1.43 0.68 0.45 -0.76 0.43 -2.29
2 8 3 8 182 0.09 -0.47 2.30 0.49 -0.05 0.43 -0.85
2 8 4 10 236 0.19 -0.61 2.30 0.49 -0.05 -0.67 -1.01
2 8 5 13 87 0.15 -0.66 2.30 1.70 -0.05 -0.16 -2.28
2 8 6 4 117 0.13 -1.29 0.49 2.29 -0.76 -0.67 -2.17
2 8 7 2 64 0.02 -1.12 2.30 2.29 -0.76 -0.67 -2.37
2 8 8 3 104 0.06 -0.17 2.30 2.29 -0.05 -0.67 -0.98
2 8 9 4 170 0.08 -0.90 1.11 1.35 -0.05 0.43 -1.21
2 8 10 7 146 0.07 -0.91 2.30 0.47 -0.05 -0.67 -2.34
2 8 11 12 409 0.11 -0.78 2.30 -0.33 -0.76 -0.67 -1.03
2 8 12 7 241 0.1 -0.19 2.30 0.33 -0.05 -0.67 -0.89
2 8 13 4 258 0.09 0.04 2.30 -0.08 -0.05 -0.67 -1.04
2 8 14 9 330 0.09 -1.17 2.30 0.45 -0.76 -0.67 -2.26
2 8 15 6 212 0.13 -0.74 0.68 0.30 -0.05 0.43 -2.40
2 8 16 7 175 0.07 -0.53 2.30 0.49 -0.05 0.43 -1.23
2 8 17 4 109 0.04 -0.38 2.30 1.70 -0.05 0.43 -1.05
2 8 18 10 144 0.09 -0.89 0.68 1.70 -0.05 -0.67 -2.20
2 8 19 1 283 0 -1.59 0.68 -0.19 -0.05 0.43 -2.29
2 8 20 7 123 0.17 -0.94 2.30 0.46 -0.35 0.43 -2.27
2 8 21 3 329 0.06 -0.86 2.30 -0.29 -0.76 0.43 -0.98
2 8 22 21 277 0.11 -1.16 0.68 0.48 -0.05 -0.67 -2.25
2 8 23 0 NA NA NA NA NA NA NA NA
2 9 1 33 331 0.22 -0.57 -0.08 0.41 -0.05 -0.67 -0.71
2 9 2 10 368 0.19 -0.75 0.68 -0.60 -0.76 0.43 -0.42
2 9 3 13 423 0.19 -1.02 0.68 -0.69 -0.70 -0.67 -0.83
2 9 4 8 335 0.2 -0.08 0.68 -0.49 -0.23 -0.67 -0.86
2 9 5 15 377 0.21 -1.31 -0.08 0.30 -0.76 0.43 -0.98
2 9 6 8 224 0.04 -0.74 1.11 0.50 -0.05 0.43 -1.22
2 9 7 22 261 0.13 -0.22 0.68 0.29 -0.05 0.43 -0.60
2 9 8 14 381 0.28 -0.89 0.57 -0.09 -0.51 -0.67 -0.23
2 9 9 14 257 0.08 -0.64 0.68 0.49 -0.05 0.43 -0.76
2 9 10 13 354 0.27 -1.37 0.33 0.47 -0.27 -0.67 -0.93
2 9 11 9 248 0.16 -1.00 0.68 0.57 -0.05 0.43 -1.22
2 9 12 23 323 0.13 -0.51 0.68 0.02 -0.05 -0.67 -0.46
2 9 13 10 344 0.25 -1.39 0.68 -0.30 -0.48 0.43 -1.23
2 9 14 11 267 0.11 -1.03 0.68 0.41 -0.05 0.43 -0.85
2 9 15 20 422 0.17 -1.43 0.68 -0.23 -0.72 -0.67 -1.02
2 9 16 23 206 0.26 -0.52 0.70 1.25 -0.05 0.43 -0.79
2 9 17 8 304 0.13 -0.86 0.68 -0.12 -0.05 0.43 -0.39
2 9 18 8 240 0.05 -0.72 1.11 0.50 -0.05 0.43 -0.83
2 9 19 32 303 0.35 -0.82 0.68 0.33 0.04 -0.67 -1.07
2 9 20 13 317 0.16 -1.11 0.68 0.34 -0.76 0.43 -0.90
2 9 21 10 308 0.22 -0.75 -0.24 0.33 -0.05 0.43 -0.69
2 9 22 33 296 0.2 -0.39 0.68 0.55 -0.05 -0.67 -0.56
2 9 23 3 196 0.03 -0.83 -0.08 1.70 -0.05 -0.67 -1.98
2 10 1 4 269 0.07 0.51 0.68 -0.55 -0.05 0.43 -0.62
2 10 2 8 327 0.1 -0.43 0.68 -0.12 -0.05 0.43 1.46
2 10 3 23 318 0.15 0.23 -0.08 -0.23 -0.05 0.43 0.69
2 10 4 3 346 0.12 -0.04 0.68 -0.74 -0.76 0.43 -0.31
2 10 5 9 271 0.17 0.14 0.73 0.34 -0.05 0.43 1.57
2 10 6 10 273 0.12 0.92 0.68 -0.54 -0.05 0.43 0.74
2 10 7 9 299 0.11 0.93 -0.08 -0.36 -0.05 0.43 0.66
2 10 8 6 307 0.08 -0.01 0.68 -0.52 -0.05 0.43 0.38
2 10 9 8 289 0.15 0.67 -0.08 -0.27 -0.05 0.43 -0.15
2 10 10 13 325 0.26 0.16 -0.08 0.00 -0.16 0.43 1.23
2 10 11 13 315 0.18 -0.46 0.68 -0.14 -0.05 0.43 0.64
2 10 12 10 259 0.12 0.83 0.68 -0.14 -0.05 0.43 0.32
2 10 13 7 234 0.06 -0.20 0.68 1.23 -0.05 0.43 0.35
2 10 14 12 260 0.16 0.74 0.72 0.08 -0.05 0.43 0.89
2 10 15 8 249 0.12 0.66 0.68 0.48 -0.14 0.43 0.81
2 10 16 13 268 0.09 0.04 0.68 0.49 -0.05 0.43 0.60
2 10 17 11 256 0.11 0.31 0.68 0.24 -0.05 0.43 -0.06
2 10 18 6 342 0.17 0.82 0.30 -0.76 -0.76 0.43 0.64
2 10 19 8 302 0.15 0.22 0.68 -0.33 -0.05 0.43 1.20
2 10 20 12 370 0.24 -0.28 0.75 -0.51 -0.76 0.43 0.84
2 10 21 19 281 0.11 0.29 0.68 -0.07 -0.05 0.43 0.64
2 10 22 9 290 0.13 -0.34 0.68 0.15 -0.05 0.43 0.20
2 10 23 13 351 0.11 0.21 0.68 -0.70 -0.76 0.43 0.66
2 11 1 10 411 0.22 -1.09 -0.93 0.23 -0.12 -0.67 -0.72
2 11 2 14 502 0.14 -1.13 -0.97 -1.01 -0.86 -0.67 -0.09
2 11 3 7 481 0.2 -0.81 -0.08 -1.20 -1.11 -0.36 -0.96
2 11 4 19 516 0.16 -0.95 -0.95 -1.13 -0.91 -0.67 -1.64
2 11 5 14 482 0.12 -1.58 -0.89 -0.16 -0.76 -0.67 -0.68
2 11 6 24 498 0.16 -1.36 -0.94 -0.85 -0.77 -0.67 -0.46
2 11 7 17 527 0.25 -1.29 -1.25 -1.06 -0.84 -0.61 -1.65
2 11 8 23 484 0.15 -1.01 -0.92 -0.84 -0.79 -0.67 -0.72
2 11 9 18 509 0.1 -1.67 -0.91 -0.78 -0.76 -0.67 -0.75
2 11 10 10 435 0.15 -0.94 -0.08 -0.59 -0.69 -0.67 -0.89
2 11 11 19 491 0.25 -1.54 -0.93 -0.50 -0.74 -0.67 -0.11
2 11 12 12 452 0.25 -1.47 -0.76 -0.12 -0.79 0.43 -0.55
2 11 13 8 445 0.17 -1.22 -0.08 -0.43 -0.67 -0.67 -0.19
2 11 14 8 427 0.08 -0.60 -0.89 -0.75 -0.05 -0.67 -0.70
2 11 15 17 466 0.16 -0.52 -0.98 -0.84 -0.76 -0.67 -0.67
2 11 16 17 511 0.16 -1.09 -1.00 -1.06 -0.88 -0.67 -1.12
2 11 17 8 437 0.08 -0.69 -0.08 -0.75 -0.76 -0.67 -0.48
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2 11 19 10 525 0.18 -1.69 -1.19 -1.13 -0.90 -0.67 -0.23
2 11 20 30 473 0.29 -1.06 -0.87 -0.89 -0.79 0.43 -0.61
2 11 21 6 450 0.1 -1.62 -0.08 -0.06 -0.76 -0.67 -0.70
2 11 22 18 457 0.26 -1.05 -0.89 -0.10 -0.68 -0.67 -0.16
2 11 23 12 453 0.09 -1.43 -0.08 -0.29 -0.76 -0.67 -1.02
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2 12 2 13 394 0.18 -0.08 0.68 -0.81 -0.79 -0.67 -0.16
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2 12 5 15 442 0.11 -0.32 0.68 -1.19 -1.09 -0.67 0.31
2 12 6 12 458 0.26 -0.88 0.68 -0.73 -0.70 -0.67 1.24
2 12 7 17 405 0.25 -0.57 0.68 -0.86 -0.90 0.43 0.44
2 12 8 23 421 0.14 0.08 -0.08 -0.77 -0.76 -0.67 0.62
2 12 9 24 468 0.16 -0.66 -0.08 -1.13 -0.98 -0.67 0.37
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2 12 11 8 449 0.09 -0.21 0.84 -0.78 -0.76 -0.67 1.57
2 12 12 10 454 0.22 -0.75 0.72 -0.93 -0.94 0.43 1.25
2 12 13 19 428 0.17 -0.83 -0.08 -0.26 -0.68 -0.67 0.55
2 12 14 8 506 0.12 -0.51 1.05 -1.19 -1.11 -0.67 1.36
2 12 15 9 443 0.16 -0.77 -0.08 -0.08 -0.76 -0.67 1.22
2 12 16 21 441 0.19 -0.46 -0.08 -0.80 -0.62 -0.67 0.85
2 12 17 21 436 0.14 -0.85 0.68 -0.87 -0.76 -0.67 0.44
2 12 18 27 492 0.15 -0.84 -0.08 -1.17 -1.05 -0.67 0.90
2 12 19 9 495 0.15 -0.81 -0.08 -0.91 -0.88 -0.67 1.48
2 12 20 19 431 0.24 -0.99 0.68 -0.80 -0.78 -0.67 -0.34
2 12 21 16 387 0.2 -0.62 0.68 -0.11 -0.67 -0.67 0.49
2 12 22 10 477 0.19 -0.79 -0.08 -1.19 -1.11 0.43 0.74
2 12 23 27 415 0.13 -0.11 0.76 -0.76 -0.76 -0.67 1.01
2 13 1 10 138 0.21 0.94 0.68 0.67 1.37 0.43 -0.06
2 13 2 14 131 0.21 2.10 0.68 0.25 1.37 0.43 0.77
2 13 3 4 198 0.02 0.61 0.68 0.45 1.37 -0.67 0.69
2 13 4 2 47 0.19 1.96 1.49 2.29 1.37 0.43 1.36
2 13 5 8 143 0.08 1.28 1.11 0.45 1.37 -0.67 1.36
2 13 6 4 98 0.2 0.98 2.30 0.73 1.37 0.43 0.00
2 13 7 10 155 0.13 1.55 0.68 -0.28 1.37 0.43 0.33
2 13 8 24 151 0.12 1.45 0.68 0.22 1.37 0.43 0.72
2 13 9 5 164 0.11 1.30 -0.08 0.40 1.37 0.43 0.73
2 13 10 12 176 0.12 1.08 0.68 -0.15 1.37 0.43 0.72
2 13 11 10 94 0.13 1.39 2.30 0.44 1.37 0.43 1.23
2 13 12 12 154 0.12 1.75 0.68 0.36 1.37 -0.67 0.29
2 13 13 4 174 0.1 0.56 0.68 0.82 1.37 -0.67 0.19
2 13 14 18 153 0.27 0.89 0.75 0.30 1.37 0.43 1.33
2 13 15 10 172 0.22 0.58 0.77 0.34 1.37 0.43 0.47
2 13 16 8 177 0.08 0.88 0.68 0.45 1.37 -0.67 1.41
2 13 17 2 125 0.09 2.71 0.68 0.34 1.37 -0.67 0.67
2 13 18 8 95 0.07 1.62 2.30 0.45 1.37 -0.67 1.41
2 13 19 7 173 0.07 1.27 0.68 0.45 1.37 -0.67 0.74
2 13 20 7 128 0.1 1.78 0.68 0.38 1.37 0.43 -0.02
2 13 21 16 111 0.2 1.15 2.30 0.59 1.37 -0.67 0.18
2 13 22 10 152 0.11 1.78 0.68 0.46 1.37 -0.67 0.90
2 13 23 4 162 0.07 1.30 0.68 0.46 1.37 -0.67 0.05
2 14 1 46 475 0.08 -0.74 -0.89 -0.78 -0.76 -0.67 0.52
2 14 2 36 469 0.16 -0.24 -0.94 -0.83 -0.76 -0.67 0.94
2 14 3 19 439 0.18 -0.52 -0.95 -0.74 -0.05 -0.67 0.60
2 14 4 13 459 0.15 0.21 -1.04 -0.93 -0.76 -0.67 0.60
2 14 5 24 501 0.14 -0.59 -1.00 -1.16 -0.89 -0.67 0.87
2 14 6 44 480 0.13 -0.63 -0.93 -0.78 -0.76 -0.67 0.98
2 14 7 35 493 0.13 -0.68 -0.91 -1.17 -0.98 -0.67 0.42
2 14 8 19 451 0.1 -0.20 -0.95 -0.74 -0.76 -0.67 -0.06
2 14 9 19 483 0.14 -0.72 -1.03 -0.93 -0.85 -0.67 -0.07
2 14 10 34 488 0.13 -0.61 -1.27 -0.93 -0.76 -0.67 0.54
2 14 11 11 455 0.18 -0.85 -0.89 -0.17 -0.69 -0.67 0.45
2 14 12 37 462 0.1 -0.26 -0.91 -0.85 -0.76 -0.67 0.39
2 14 13 0 NA NA NA NA NA NA NA NA
2 14 14 0 NA NA NA NA NA NA NA NA
2 14 15 0 NA NA NA NA NA NA NA NA
2 14 16 0 NA NA NA NA NA NA NA NA
2 14 17 0 NA NA NA NA NA NA NA NA
2 14 18 0 NA NA NA NA NA NA NA NA
2 14 19 0 NA NA NA NA NA NA NA NA
2 14 20 0 NA NA NA NA NA NA NA NA
2 14 21 0 NA NA NA NA NA NA NA NA
2 14 22 0 NA NA NA NA NA NA NA NA
2 14 23 0 NA NA NA NA NA NA NA NA
2 15 1 13 341 0.17 0.19 -0.92 -0.52 -0.05 0.43 -0.93
2 15 2 16 361 0.16 0.24 0.68 -0.91 -0.45 -0.67 -1.62
2 15 3 5 456 0.11 -0.29 -0.89 -0.70 -0.76 -0.67 -1.12
2 15 4 26 461 0.2 -0.35 -0.08 -1.04 -0.81 -0.67 -1.59
2 15 5 16 444 0.3 -0.40 0.68 -1.15 -0.94 -0.61 -1.48
2 15 6 15 486 0.08 -0.50 -0.89 -0.92 -0.76 -0.67 -1.66
2 15 7 5 203 0.2 0.69 -1.12 -0.43 1.37 -0.23 -1.58
2 15 8 9 426 0.33 -0.40 -0.75 -0.77 -0.68 0.43 -1.23
2 15 9 14 369 0.19 0.28 -0.92 -0.38 -0.05 -0.67 -0.90
2 15 10 11 464 0.07 -0.06 -0.89 -0.82 -0.76 -0.67 -1.66
2 15 11 5 460 0.11 0.54 -0.89 -0.88 -0.76 -0.67 -1.70
2 15 12 7 410 0.17 0.51 -0.08 -0.92 -0.76 -0.67 -1.57
2 15 13 17 352 0.15 0.35 -0.89 -0.72 -0.13 0.43 -1.66
2 15 14 11 420 0.08 0.02 -1.03 -0.67 -0.05 -0.67 -1.65
2 15 15 13 396 0.13 0.43 -0.89 -0.71 -0.05 -0.67 -1.63
2 15 16 4 379 0.23 0.75 -0.69 -0.65 -0.76 0.15 -0.67
2 15 17 7 322 0.21 0.47 0.24 -0.72 -0.66 0.43 -1.52
2 15 18 25 343 0.22 0.36 -0.08 -0.63 -0.05 -0.67 -1.53
2 15 19 15 496 0.09 -0.38 -1.04 -1.11 -0.76 -0.67 -1.63
2 15 20 14 380 0.3 0.03 -0.08 -0.55 -0.46 -0.67 -0.82
2 15 21 14 293 0.21 0.50 -0.08 -0.67 -0.05 0.43 -1.14
2 15 22 10 353 0.17 0.20 0.68 -0.81 -0.48 -0.67 -0.92
2 15 23 11 432 0.09 -0.35 -0.89 -0.80 -0.05 -0.67 -1.61
2 16 1 8 58 0.25 0.04 2.30 1.70 -0.05 2.64 -1.20
2 16 2 1 33 0 1.25 2.30 1.20 1.37 2.64 -0.94
2 16 3 13 90 0.39 0.07 2.30 0.48 -0.05 2.64 -0.99
2 16 4 5 230 0.11 0.87 -0.89 -0.67 -0.33 2.64 -1.64
2 16 5 11 163 0.15 -0.13 0.68 0.38 -0.05 2.64 -0.78
2 16 6 4 75 0.04 0.84 -0.89 1.20 1.37 2.64 -0.83
2 16 7 17 207 0.2 -0.62 0.68 0.36 -0.76 2.64 -1.01
2 16 8 20 135 0.14 -0.24 0.98 0.51 -0.05 2.64 -1.10
2 16 9 9 132 0.15 1.33 -0.08 -0.65 -0.29 2.64 -1.52
2 16 10 8 74 0.2 0.95 0.39 1.10 1.37 2.64 -0.65
2 16 11 8 284 0.05 -0.76 -0.08 0.51 -0.76 2.64 -1.16
2 16 12 5 83 0.04 0.78 -0.89 1.20 1.37 2.64 -0.43
2 16 13 5 105 0.07 -0.44 0.68 0.49 -0.05 2.64 -2.23
2 16 14 4 136 0.09 1.24 0.68 -0.64 -0.05 2.64 -0.87
2 16 15 2 106 0.03 1.56 0.68 -0.71 -0.76 2.64 -1.71
2 16 16 9 120 0.06 -0.01 0.68 1.23 -0.05 2.64 -0.72
2 16 17 7 67 0.21 0.47 0.41 1.49 1.37 2.64 -0.97
2 16 18 7 213 0.33 0.07 0.57 -0.21 -0.05 2.64 -0.36
2 16 19 5 160 0.15 0.43 0.68 0.62 -0.05 2.64 0.17
2 16 20 6 320 0.13 -0.58 0.68 -0.26 -0.76 2.64 -0.44
2 16 21 3 85 0.06 0.38 0.68 2.29 -0.05 2.64 -0.61
2 16 22 6 345 0.1 -0.82 -0.08 0.21 -0.76 2.64 -0.79
2 16 23 5 110 0.06 1.39 0.68 -0.67 -0.05 2.64 -1.61
2 17 1 6 440 0.09 -0.58 -1.27 0.12 -0.05 -0.67 1.29
2 17 2 10 416 0.13 -0.58 -0.93 -0.18 -0.05 -0.67 0.64
2 17 3 12 417 0.09 -0.24 -0.92 0.15 -0.05 -0.67 1.57
2 17 4 9 349 0.12 0.29 -0.93 0.23 -0.05 -0.67 -0.11
2 17 5 5 309 0.28 0.52 -0.89 0.35 -0.05 0.43 0.52
2 17 6 16 385 0.13 0.31 -0.89 -0.45 -0.05 -0.67 0.41
2 17 7 23 372 0.09 0.31 -0.91 0.03 -0.05 -0.67 0.86
2 17 8 21 403 0.09 -0.15 -1.27 0.09 -0.05 -0.67 0.85
2 17 9 14 366 0.13 -0.37 -0.92 0.45 -0.05 -0.67 -0.31
2 17 10 11 419 0.13 -0.26 -0.89 -0.36 -0.05 -0.67 1.02
2 17 11 13 389 0.11 -0.35 -0.95 0.02 -0.05 -0.67 0.00
2 17 12 17 392 0.06 -0.26 -0.89 0.05 -0.05 -0.67 0.62
2 17 13 4 362 0.17 0.15 -1.08 0.01 -0.05 -0.67 -0.67
2 17 14 9 424 0.17 0.37 -0.89 -0.29 -0.76 -0.67 0.90
2 17 15 12 395 0.09 -0.06 -1.27 -0.09 -0.05 -0.67 0.37
2 17 16 18 399 0.11 -0.17 -0.89 0.09 -0.05 -0.67 1.05
2 17 17 15 373 0.09 -0.59 -0.89 0.45 -0.05 -0.67 -0.58
2 17 18 11 357 0.09 0.20 -0.89 0.47 -0.05 -0.67 0.68
2 17 19 15 398 0.26 0.98 -0.89 -0.41 -0.57 -0.67 0.49
2 17 20 20 367 0.08 0.25 -0.91 0.05 -0.05 -0.67 0.46
2 17 21 3 438 0.08 -0.60 -0.89 0.04 -0.76 -0.67 0.48
2 17 22 6 429 0.08 -0.22 -0.89 -0.07 -0.76 -0.67 0.68
2 17 23 15 382 0.08 -0.35 -0.92 0.45 -0.05 -0.67 0.47
2 18 1 4 430 0.06 -0.12 2.30 -0.78 -0.76 -0.67 0.52
2 18 2 5 199 0.07 0.53 2.30 0.46 -0.05 0.43 0.62
2 18 3 4 276 0.04 -0.21 2.30 0.03 -0.05 -0.67 -0.48
2 18 4 1 225 0 0.74 2.30 -0.19 -0.05 -0.67 -0.79
2 18 5 4 340 0.08 0.42 2.30 -0.56 -0.76 -0.67 -0.64
2 18 6 16 286 0.15 0.56 2.30 0.00 -0.05 -0.67 1.49
2 18 7 5 242 0.04 0.41 2.30 0.45 -0.05 -0.67 0.35
2 18 8 7 187 0.09 0.61 2.30 0.31 -0.05 0.43 1.57
2 18 9 8 200 0.15 0.62 2.30 0.08 -0.05 0.43 0.04
2 18 10 5 226 0.04 0.41 2.30 0.05 -0.05 0.43 0.69
2 18 11 8 463 0.07 0.24 2.30 -0.78 -0.76 -0.67 1.30
2 18 12 9 522 0.08 -0.14 2.30 -1.19 -1.11 -0.67 1.33
2 18 13 2 115 0.08 1.74 2.30 1.23 -0.05 -0.67 -0.03
2 18 14 6 274 0.18 0.31 2.30 -0.06 -0.05 -0.67 0.15
2 18 15 3 229 0.06 0.55 2.30 -0.06 -0.05 0.43 1.14
2 18 16 10 254 0.13 0.67 2.30 0.22 -0.05 -0.67 0.87
2 18 17 4 407 0.13 0.00 2.30 -0.78 -0.76 0.43 0.94
2 18 18 7 246 0.08 0.16 2.30 -0.04 -0.05 0.43 1.57
2 18 19 4 339 0.04 -0.04 2.30 0.05 -0.76 -0.67 0.04
2 18 20 3 217 0.01 0.65 2.30 0.03 -0.05 0.43 0.69
2 18 21 3 476 0.14 -0.52 2.30 -0.45 -0.76 -0.67 1.29
2 18 22 0 NA NA NA NA NA NA NA NA
2 18 23 0 NA NA NA NA NA NA NA NA
2 19 1 6 391 0.18 0.52 -0.89 -0.34 -0.64 0.43 0.98
2 19 2 6 383 0.07 0.68 -0.89 -0.56 -0.76 0.43 0.10
2 19 3 21 470 0.12 -1.02 -0.91 -0.76 -0.76 0.43 0.53
2 19 4 11 348 0.2 0.08 -1.03 -0.10 -0.05 0.43 0.14
2 19 5 10 446 0.15 -1.12 -0.81 -0.30 -0.76 0.43 0.01
2 19 6 14 350 0.08 0.07 -0.89 0.05 -0.05 0.43 0.74
2 19 7 8 388 0.27 -0.53 -0.38 -0.56 -0.40 0.43 -0.28
2 19 8 7 467 0.11 -1.18 -0.89 -0.29 -0.76 0.43 0.88
2 19 9 6 425 0.09 -0.49 -0.89 -0.23 -0.76 0.43 0.58
2 19 10 9 406 0.1 -0.18 -0.08 -0.75 -0.76 0.43 0.63
2 19 11 10 400 0.16 -0.36 -0.89 -0.71 -0.05 0.43 0.33
2 19 12 9 347 0.21 -0.22 -0.89 0.49 -0.13 0.43 0.63
2 19 13 8 497 0.1 -0.83 -0.89 -1.19 -1.11 0.43 0.44
2 19 14 16 378 0.12 -0.25 -1.03 -0.12 -0.05 0.43 0.74
2 19 15 16 418 0.15 -0.73 -0.08 -0.41 -0.76 0.43 0.82
2 19 16 22 448 0.15 -0.21 -0.94 -0.82 -0.76 0.43 0.77
2 19 17 13 485 0.15 -0.74 -0.95 -0.83 -0.76 0.43 1.20
2 19 18 13 447 0.14 -0.52 -0.98 -0.75 -0.76 0.43 0.17
2 19 19 10 412 0.21 -0.48 -0.81 -0.43 -0.05 0.43 1.25
2 19 20 11 355 0.16 -0.61 -0.89 0.20 -0.05 0.43 -0.14
2 19 21 9 390 0.1 -0.66 -0.89 -0.14 -0.05 0.43 0.65
2 19 22 10 401 0.15 -0.52 -0.93 0.13 -0.05 0.43 1.40
2 19 23 11 487 0.12 -0.83 -1.27 -0.86 -0.76 0.43 0.75
2 20 1 5 73 0.02 -0.13 0.68 1.70 1.37 0.43 -2.46
2 20 2 3 69 0.02 -0.02 0.68 2.29 1.37 0.43 -1.98
2 20 3 3 65 0.19 -0.83 1.22 3.07 -0.05 -0.67 -2.46
2 20 4 7 79 0.03 0.82 2.30 1.21 1.37 0.43 -0.92
2 20 5 5 62 0.03 0.13 0.68 2.29 1.37 0.43 -2.32
2 20 6 3 80 0.04 -0.03 0.68 1.70 1.37 0.43 -2.19
2 20 7 3 71 0.03 0.47 2.30 1.70 1.37 0.43 -0.79
2 20 8 2 72 0 0.22 0.68 1.70 1.37 0.43 -2.46
2 20 9 12 35 0.14 0.15 2.30 2.29 1.37 0.43 -2.29
2 20 10 4 44 0.06 -0.03 0.68 3.07 1.37 0.43 -2.25
2 20 11 11 42 0.07 0.15 2.30 1.70 1.37 0.43 -2.39
2 20 12 1 31 0 0.57 2.30 3.30 1.37 0.43 -1.25
2 20 13 5 63 0.08 -0.29 0.68 2.29 1.37 0.43 -2.35
2 20 14 6 66 0.05 0.39 2.30 1.70 1.37 0.43 -1.23
2 20 15 1 68 0 0.31 0.68 2.29 1.37 0.43 -1.98
2 20 16 3 78 0.05 1.06 2.30 1.23 1.37 0.43 -0.62
2 20 17 4 27 0.05 0.19 2.30 3.07 1.37 0.43 -2.25
2 20 18 0 NA NA NA NA NA NA NA NA
2 20 19 0 NA NA NA NA NA NA NA NA
2 20 20 0 NA NA NA NA NA NA NA NA
2 20 21 0 NA NA NA NA NA NA NA NA
2 20 22 0 NA NA NA NA NA NA NA NA
2 20 23 0 NA NA NA NA NA NA NA NA
2 21 1 4 504 0.17 0.72 -0.89 -0.66 -0.76 2.64 1.36
2 21 2 5 245 0.17 0.97 0.68 -0.65 -0.62 2.64 1.03
2 21 3 6 313 0.16 -0.20 0.68 -0.40 -0.52 2.64 0.41
2 21 4 10 338 0.18 0.27 -0.89 -0.34 -0.05 2.64 0.32
2 21 5 4 375 0.13 0.16 -0.49 0.04 -0.76 2.64 0.66
2 21 6 6 298 0.15 1.35 -0.08 -0.45 -0.76 2.64 0.94
2 21 7 10 526 0.21 -0.31 -1.08 -0.88 -0.76 2.64 1.28
2 21 8 11 490 0.15 -0.83 -0.89 -0.25 -0.76 2.64 -0.33
2 21 9 6 393 0.19 1.39 -0.89 -0.56 -0.76 2.64 -0.04
2 21 10 8 359 0.11 0.49 -0.89 -0.39 -0.05 2.64 0.95
2 21 11 6 295 0.1 0.19 -0.08 -0.29 -0.05 2.64 0.75
2 21 12 7 376 0.09 -0.05 -0.89 -0.19 -0.05 2.64 0.77
2 21 13 18 205 0.2 0.58 0.68 -0.13 -0.13 2.64 0.65
2 21 14 6 186 0.18 0.55 0.55 0.01 -0.05 2.64 1.50
2 21 15 6 328 0.14 0.27 -0.89 -0.73 -0.05 2.64 -0.76
2 21 16 2 215 0.1 0.75 -0.08 -0.46 -0.05 2.64 -0.35
2 21 17 5 408 0.12 -0.53 -0.08 -0.29 -0.76 2.64 0.19

Now let’s check the compression summary for HVT (map C). The table below shows no of cells, no of cells having quantization error below threshold and percentage of cells having quantization error below threshold for each level.

mapC_compression_summary <- map_C[[3]]$compression_summary %>%  dplyr::mutate_if(is.numeric, funs(round(.,4)))
compressionSummaryTable(mapC_compression_summary)
segmentLevel noOfCells noOfCellsBelowQuantizationError percentOfCellsBelowQuantizationErrorThreshold parameters
1 23 0 0 n_cells: 23 quant.err: 0.2 distance_metric: L1_Norm error_metric: max quant_method: kmeans
2 508 434 0.85 n_cells: 23 quant.err: 0.2 distance_metric: L1_Norm error_metric: max quant_method: kmeans

As it can be seen from the table above, 0% of the cells have hit the quantization threshold error in level 1 and 85% of the cells have hit the quantization threshold error in level 2

Let’s plot the Voronoi tessellation for layer 2 (map C)

muHVT::plotHVT(map_C,
        line.width = c(0.4,0.2), 
        color.vec = c("#141B41","#0582CA"),
        centroid.size = 0.1,
        maxDepth = 2) 
Figure 14: The Voronoi Tessellation for layer 2 (map C) shown for the 100 cells in the dataset ’computers’ at level 2

Figure 14: The Voronoi Tessellation for layer 2 (map C) shown for the 100 cells in the dataset ’computers’ at level 2

Heat Maps

Now let’s plot all the features for each cell at level two as a heatmap for better visualization.

The heatmaps displayed below provides a visual representation of the spatial characteristics of the computers data, allowing us to observe patterns and trends in the distribution of each of the features (n,price,speed,hd,ram,screen,ads). The sheer green shades highlight regions with higher values in each of the heatmaps, while the indigo shades indicate areas with the lowest values in each of the heatmaps. By analyzing these heatmaps, we can gain insights into the variations and relationships between each of these features within the computers data.


  hvtHmap(
  map_C,
  trainComputers,
  child.level = 2,
  hmap.cols = "n",
  line.width = c(0.6,0.4),
  color.vec = c("#141B41","#0582CA"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = T,
  quant.error.hmap = 0.2,
  n_cells.hmap = 100,
) 
Figure 15: The Voronoi Tessellation with the heat map overlaid for features No. of entities in each cell

Figure 15: The Voronoi Tessellation with the heat map overlaid for features No. of entities in each cell


  hvtHmap(
  map_C,
  trainComputers,
  child.level = 2,
  hmap.cols = "price",
  line.width = c(0.6,0.4),
  color.vec = c("#141B41","#0582CA"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = T,
  quant.error.hmap = 0.2,
  n_cells.hmap = 100,
) 
Figure 16: The Voronoi Tessellation with the heat map overlaid for features price in the ’computers’ dataset

Figure 16: The Voronoi Tessellation with the heat map overlaid for features price in the ’computers’ dataset


  hvtHmap(
  map_C,
  trainComputers,
  child.level = 2,
  hmap.cols = "speed",
  line.width = c(0.6,0.4),
  color.vec = c("#141B41","#0582CA"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = T,
  quant.error.hmap = 0.2,
  n_cells.hmap = 100,
) 
Figure 17: The Voronoi Tessellation with the heat map overlaid for features speed in the ’computers’ dataset

Figure 17: The Voronoi Tessellation with the heat map overlaid for features speed in the ’computers’ dataset


  hvtHmap(
  map_C,
  trainComputers,
  child.level = 2,
  hmap.cols = "hd",
  line.width = c(0.6,0.4),
  color.vec = c("#141B41","#0582CA"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = T,
  quant.error.hmap = 0.2,
  n_cells.hmap = 100,
) 
Figure 18: The Voronoi Tessellation with the heat map overlaid for features hd in the ’computers’ dataset

Figure 18: The Voronoi Tessellation with the heat map overlaid for features hd in the ’computers’ dataset


  hvtHmap(
  map_C,
  trainComputers,
  child.level = 2,
  hmap.cols = "ram",
  line.width = c(0.6,0.4),
  color.vec = c("#141B41","#0582CA"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = T,
  quant.error.hmap = 0.2,
  n_cells.hmap = 100,
) 
Figure 19: The Voronoi Tessellation with the heat map overlaid for features ram in the ’computers’ dataset

Figure 19: The Voronoi Tessellation with the heat map overlaid for features ram in the ’computers’ dataset


  hvtHmap(
  map_C,
  trainComputers,
  child.level = 2,
  hmap.cols = "screen",
  line.width = c(0.6,0.4),
  color.vec = c("#141B41","#0582CA"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = T,
  quant.error.hmap = 0.2,
  n_cells.hmap = 100,
) 
Figure 20: The Voronoi Tessellation with the heat map overlaid for features screen in the ’computers’ dataset

Figure 20: The Voronoi Tessellation with the heat map overlaid for features screen in the ’computers’ dataset


  hvtHmap(
  map_C,
  trainComputers,
  child.level = 2,
  hmap.cols = "ads",
  line.width = c(0.6,0.4),
  color.vec = c("#141B41","#0582CA"),
  palette.color = 6,
  centroid.size = 0.1,
  show.points = T,
  quant.error.hmap = 0.2,
  n_cells.hmap = 100,
) 
Figure 21: The Voronoi Tessellation with the heat map overlaid for features ads in the ’computers’ dataset

Figure 21: The Voronoi Tessellation with the heat map overlaid for features ads in the ’computers’ dataset

We now have the set of maps (map A, map B & map C) which will be used to predict which map and cell each test record is assigned to, but before that lets view our test dataset

6 Prediction on Test Data

Now once we have built the model, let us try to predict using our test dataset (containing 1252 data points) which cell and which layer each point belongs to.

Raw Testing Dataset

The testing dataset includes the following columns:

Let’s have a look at our randomly selected test dataset containing 1252 datapoints.

Table(head(testComputers_data))
Row.No price speed hd ram screen ads
3 1595 25 170 4 15 94
4 1849 25 170 8 14 94
7 1720 25 170 4 14 94
10 2575 50 210 4 15 94
11 2195 33 170 8 15 94
14 2295 25 245 8 14 94

The predictLayerHVT function is used to score the test data using the predictive set of maps. This function takes an input - a test data and a set of maps (map A, map B, map C).

Now, Let us understand the predictLayerHVT function.

predictLayerHVT(data,
                map_A,
                map_B,
                map_C,
                mad.threshold = 0.2,
                normalize = T, 
                distance_metric="L1_Norm",
                error_metric="max",
                child.level = 1, 
                line.width = c(0.6, 0.4, 0.2),
                color.vec = c("#141B41", "#6369D1", "#D8D2E1"),
                yVar= NULL,
                ...)

Each of the parameters of predictLayerHVT function has been explained below:

The function predicts based on the HVT maps - map A, map B and map C, constructed using HVT function. For each test record, the function will assign that record to Layer1 or Layer2. Layer1 contains the cell ids from map A and Layer 2 contains cell ids from map B (novelty map) and map C (map without novelty).

Prediction Algorithm

The prediction algorithm recursively calculates the distance between each point in the test dataset and the cell centroids for each level. The following steps explain the prediction method for a single point in the test dataset:

  1. Calculate the distance between the point and the centroid of all the cells in the first level.
  2. Find the cell whose centroid has minimum distance to the point.
  3. Check if the cell drills down further to form more cells.
  4. If it doesn’t, return the path. Or else repeat steps 1 to 4 till we reach a level at which the cell doesn’t drill down further.

Note : The prediction algorithm will not work if some of the variables used to perform quantization are missing. In the test dataset, we should not remove any features


validation_data <- testComputers
new_predict <- predictLayerHVT(
    data=validation_data,
    map_A,
    map_B,
    map_C,
    normalize = T
  )
summary_list <- map_A[[3]]

train_colnames <- names(summary_list[["nodes.clust"]][[1]][[1]])
scaled_test_data <- scale(
     testComputers[, train_colnames],
      center = summary_list$scale_summary$mean_data[train_colnames],
      scale = summary_list$scale_summary$std_data[train_colnames]) %>% data.frame()
      scaled_test_data$Row.No <- row.names(testComputers)
predictions <- new_predict %>%
  dplyr::select(Layer1.Cell.ID, Layer2.Cell.ID) %>%
  mutate(Cell.ID = as.numeric(gsub("[A]", "", Layer1.Cell.ID)),
  Row.No = row.names(testComputers))

merged_df <- merge(predictions,scaled_test_data, by = "Row.No", all.x = TRUE) %>%
             arrange(as.numeric(Row.No)) %>% select(Row.No, price, speed, hd, ram, screen, ads, Layer1.Cell.ID, Layer2.Cell.ID) 
  
colnames(merged_df) <- c("Row.No", "price_act", "speed_act", "hd_act", "ram_act", "screen_act", "ads_act",
                         "Layer1.Cell.ID", "Layer2.Cell.ID")

combined <- merged_df %>%
  mutate(Cell.ID = gsub("[C]", "", Layer2.Cell.ID)) %>%
  merge(map_C[[3]]$summary, by = "Cell.ID", all.x = TRUE) %>%
  arrange(as.numeric(Row.No)) %>%
  select(Row.No, price_act, speed_act, hd_act, ram_act, screen_act, ads_act, Layer1.Cell.ID, Layer2.Cell.ID,
  Segment.Level, Segment.Parent, Segment.Child, n, Quant.Error, price, speed, hd, ram, screen, ads)


merged_df <- combined %>%
             mutate(Cell.ID = gsub("[B]", "", Layer2.Cell.ID)) %>%
             merge(map_B[[3]]$summary, by = "Cell.ID", all.x = TRUE) %>%
             arrange(as.numeric(Row.No)) %>%
             select(Row.No, price_act, speed_act, hd_act, ram_act, screen_act, ads_act, Layer1.Cell.ID, Layer2.Cell.ID,
             price.x, speed.x, hd.x, ram.x, screen.x, ads.x, price.y, speed.y, hd.y, ram.y, screen.y, ads.y)%>%
             mutate(price_pred = coalesce(price.x, price.y),
             speed_pred = coalesce(speed.x, speed.y),
             hd_pred = coalesce(hd.x, hd.y),
             ram_pred = coalesce(ram.x, ram.y),
             screen_pred = coalesce(screen.x, screen.y),
             ads_pred = coalesce(ads.x, ads.y)) %>%
             select(Row.No, price_act, speed_act, hd_act, ram_act, screen_act, ads_act, Layer1.Cell.ID, Layer2.Cell.ID,
             price_pred, speed_pred, hd_pred, ram_pred, screen_pred, ads_pred)

Let’s see which cell and layer each point belongs to and check the Mean Absolute Difference for each of the 1252 records.

sorted_df <- merged_df
sorted_df$diff <- rowMeans(abs(sorted_df[, c("price_act","speed_act","hd_act","ram_act","screen_act","ads_act")] - sorted_df[, c("price_pred","speed_pred","hd_pred","ram_pred","screen_pred","ads_pred")]))
rownames(sorted_df) <- NULL
options(scipen = 999)
sorted_df %>% head(1000) %>%as.data.frame() %>%Table(scroll = T)
Row.No price_act speed_act hd_act ram_act screen_act ads_act Layer1.Cell.ID Layer2.Cell.ID price_pred speed_pred hd_pred ram_pred screen_pred ads_pred diff
3 -1.0785679 -1.2710382 -0.9472574 -0.7589986 0.4307274 -1.7213059 A24 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.4690860
4 -0.6386691 -1.2710382 -0.9472574 -0.0501185 -0.6741149 -1.7213059 A143 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.4423148
7 -0.8620823 -1.2710382 -0.9472574 -0.7589986 -0.6741149 -1.7213059 A29 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.3712467
10 0.6186793 -0.0817113 -0.7914378 -0.7589986 0.4307274 -1.7213059 A237 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3987279
11 -0.0394370 -0.8904536 -0.9472574 -0.0501185 0.4307274 -1.7213059 A223 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3772636
14 0.1337515 -1.2710382 -0.6550957 -0.0501185 -0.6741149 -1.7213059 A162 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3302613
15 0.8334330 -0.0817113 -0.7836469 -0.0501185 -0.6741149 -1.7213059 A215 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3328827
19 -0.2126255 -0.8904536 -0.6356183 -0.7589986 0.4307274 -1.7213059 A165 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.4049168
22 0.9996940 0.6794579 -1.1030770 -0.7589986 -0.6741149 -1.7213059 A214 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.5427801
24 1.1382448 -0.0817113 -0.7914378 -0.7589986 2.6404120 -1.7213059 A379 C360 0.2356188 -0.4603485 -0.3744382 -0.4107768 2.6404120 0.5948051 0.7270993
28 3.0779559 -0.8904536 0.1512706 -0.0501185 -0.6741149 -1.7213059 A367 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.7242998
29 1.5192595 -0.8904536 -0.2850242 1.3676416 -0.6741149 -1.7213059 A316 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.5546423
33 0.6533170 -0.8904536 -0.7914378 -0.0501185 2.6404120 -1.7213059 A343 C360 0.2356188 -0.4603485 -0.3744382 -0.4107768 2.6404120 0.5948051 0.6569287
39 0.3242589 -0.0817113 -0.7914378 -0.0501185 -0.6741149 -1.7213059 A215 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.2493188
40 0.3588966 -0.0817113 -0.7914378 -0.0501185 -0.6741149 -1.7213059 A215 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.2550918
43 0.4870561 -0.8904536 -0.7836469 -0.0501185 -0.6741149 -1.7213059 A187 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3049914
46 0.8265055 -0.8904536 -0.6550957 -0.0501185 -0.6741149 -1.7213059 A187 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3822895
48 -0.8118576 -1.2710382 -1.1420319 -0.7589986 -0.6741149 -1.7213059 A29 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.4120799
53 1.3460710 0.6794579 -0.2850242 -0.0501185 0.4307274 -1.7213059 A330 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.3298528
62 -0.7321909 -0.8904536 -0.9472574 -0.7589986 0.4307274 -1.7213059 A24 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.4633848
73 -0.9053794 -0.8904536 -0.9472574 -0.7589986 -0.6741149 -1.7213059 A43 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.3005997
74 1.4309333 -0.0817113 -0.6550957 -0.0501185 -0.6741149 -1.7213059 A215 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.3679198
80 -1.0196838 -1.2710382 -1.2978514 -0.0501185 -0.6741149 -1.7213059 A10 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.5204847
85 0.6533170 -1.2710382 -0.6550957 -0.0501185 -0.6741149 -1.7213059 A187 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.4168555
86 -0.3788864 -0.8904536 -1.1420319 -0.0501185 -0.6741149 -1.7213059 A143 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3680494
93 0.3502371 -0.8904536 -0.9472574 -0.0501185 0.4307274 -1.7213059 A223 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.4077083
99 0.6533170 -1.2710382 -0.2850242 1.3676416 -0.6741149 -1.7078621 A316 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.6314472
100 -0.9053794 -0.8904536 -0.9472574 -0.7589986 -0.6741149 -1.7078621 A43 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.2983591
104 1.3529985 0.6794579 -0.3239791 -0.7589986 0.4307274 -1.7078621 A330 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.4510968
106 1.3460710 0.6794579 -0.6356183 -0.0501185 2.6404120 -1.7078621 A386 C142 0.1328959 0.6627507 0.4814828 -0.0248014 2.6404120 -0.9712527 0.5181517
110 -0.1260312 0.6794579 -0.9472574 -0.7589986 -0.6741149 -1.7078621 A166 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3903145
111 1.3460710 0.6794579 -0.2850242 -0.0501185 0.4307274 -1.7078621 A330 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.3276122
115 -1.2448289 -1.2710382 -0.9472574 -0.7589986 -0.6741149 -1.7078621 A10 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.3258541
118 0.1857081 0.6794579 -0.6356183 -0.0501185 -0.6741149 -1.7078621 A250 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3735189
133 0.0038602 -0.8904536 -0.6356183 -0.7589986 -0.6741149 -1.7078621 A121 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.2683436
157 1.3529985 -0.0817113 -0.9472574 -0.7589986 -0.6741149 -1.7078621 A214 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.4465921
158 -0.0394370 -0.8904536 -0.9472574 -0.0501185 0.4307274 -1.7078621 A223 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3750230
160 2.0457525 0.6794579 -0.7135281 -0.7589986 0.4307274 -1.7078621 A330 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.5576366
168 0.6602445 -0.0817113 -0.7914378 -0.7589986 -0.6741149 -1.7078621 A214 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3051632
174 0.9113679 0.6794579 -0.6550957 -0.0501185 -0.6741149 -1.7078621 A250 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.4014194
175 2.7315789 -0.8904536 0.1512706 -0.0501185 -0.6741149 -1.7078621 A367 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.6643296
176 0.9130997 0.6794579 -0.6356183 -0.7589986 0.4307274 -1.7078621 A292 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.5763531
177 0.3138676 -0.0817113 -0.7836469 -0.7589986 -0.6741149 -1.7078621 A126 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.2461352
184 0.7381794 -0.0817113 -0.6550957 -0.0501185 -0.6741149 -1.7078621 A215 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3354896
188 0.6186793 0.6794579 -0.6356183 -0.0501185 -0.6741149 -1.7078621 A250 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.4456807
189 0.8265055 -0.8904536 -0.2850242 1.3676416 -0.6741149 -1.7078621 A316 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.5391517
190 1.3529985 0.6794579 -0.6550957 1.3676416 0.4307274 -1.6406430 A370 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.5052647
202 0.9823751 -0.8904536 -0.6356183 -0.0501185 2.6404120 -1.6406430 A343 C360 0.2356188 -0.4603485 -0.3744382 -0.4107768 2.6404120 0.5948051 0.6723580
205 -1.0785679 -0.8904536 -1.2783740 -1.1134387 -0.6741149 -1.6406430 A6 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.3725506
208 2.7315789 -0.8904536 0.1512706 -0.0501185 -0.6741149 -1.6406430 A367 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.6531265
210 2.9047674 0.6794579 0.3382540 -0.0501185 0.4307274 -1.6406430 A382 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.5878326
221 0.7225924 -0.8904536 -0.6356183 -0.0501185 2.6404120 -1.6406430 A343 C360 0.2356188 -0.4603485 -0.3744382 -0.4107768 2.6404120 0.5948051 0.6290609
225 0.6602445 -0.0817113 -0.7836469 -0.0501185 -0.6741149 -1.6406430 A215 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.2905741
226 0.9130997 0.6794579 -0.9472574 -0.0501185 -0.6741149 -1.6406430 A250 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.4386212
228 1.1728825 -0.0817113 -0.2850242 1.3676416 -0.6741149 -1.6406430 A366 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.4641376
233 -0.3788864 -0.8904536 -0.9472574 -0.7589986 -0.6741149 -1.6406430 A85 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3242305
235 -0.0394370 -1.2710382 -0.6550957 -0.0501185 -0.6741149 -1.6406430 A162 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3224537
237 -1.0785679 -1.2710382 -0.9472574 -0.7589986 0.4307274 -1.6406430 A24 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.4556422
245 0.6186793 0.6794579 -0.6356183 -0.0501185 -0.6741149 -1.6406430 A250 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.4344775
247 1.8725640 0.6794579 -0.6550957 1.3676416 0.4307274 -1.6406430 A370 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.5180150
248 0.8334330 0.6794579 -0.7797514 -0.0501185 -0.6741149 -1.6406430 A250 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.4239813
254 -0.8620823 -1.2710382 -0.9472574 -0.7589986 -0.6741149 -1.6406430 A29 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.3578029
282 -0.3858139 -0.8904536 -0.6356183 -0.7589986 -0.6741149 -1.6406430 A85 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3220861
283 0.1406791 -0.0817113 -0.7836469 -0.7589986 -0.6741149 -1.6406430 A126 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.2060673
285 0.5667228 0.6794579 -0.6356183 -0.0501185 0.4307274 -1.6406430 A292 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.5047327
308 0.1164327 -0.0817113 -0.6356183 -0.0501185 -0.6741149 -1.5330924 A215 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.2059831
310 2.7315789 -0.8904536 0.1512706 -0.0501185 -0.6741149 -1.5330924 A367 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.6352014
312 0.6602445 -0.0817113 -0.7836469 -0.0501185 -0.6741149 -1.5330924 A215 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.2726490
313 1.1728825 -0.0817113 -0.2850242 1.3676416 -0.6741149 -1.5330924 A366 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.4462125
320 -0.0394370 0.6794579 -0.9472574 -0.7589986 -0.6741149 -1.5330924 A166 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3467538
325 -0.9140388 -0.8904536 -1.2783740 -1.1134387 -0.6741149 -1.5330924 A6 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.3820470
329 1.5106000 0.6794579 -0.2850242 1.3676416 -0.6741149 -1.5330924 A366 C201 1.5745305 0.4514353 -0.2367672 0.2737663 -0.3026593 -1.3041998 0.3390723
330 0.6602445 -0.8904536 -0.6745732 -0.7589986 0.4307274 -1.5330924 A165 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.4203032
332 -0.0394370 -0.0817113 -1.1030770 -0.7589986 -0.6741149 -1.5330924 A126 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.2458622
348 0.6533170 -0.0817113 -0.6356183 -0.0501185 0.4307274 -1.5330924 A261 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3937154
349 0.5147662 -0.8904536 -0.6356183 -0.0501185 0.4307274 -1.5330924 A223 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.4004619
355 -0.2472631 0.6794579 -0.9472574 -0.7589986 -0.6741149 -1.5330924 A166 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3813915
356 1.0066215 -0.0817113 -0.6745732 -0.7589986 0.4307274 -1.5330924 A237 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.4481944
360 0.1337515 -0.8904536 -0.6550957 -0.0501185 -0.6741149 -1.5330924 A162 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.2354616
380 -1.2604158 -1.2710382 -1.2783740 -1.1134387 -0.6741149 -1.5330924 A6 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.4135831
389 -1.4249449 -1.2710382 -1.2783740 -1.1134387 -0.6741149 -1.5330924 A6 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.4410046
397 0.4004618 -0.8904536 -0.7135281 -0.7589986 -0.6741149 -1.5330924 A121 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.2722620
399 -0.5520749 -0.8904536 -0.7836469 -0.7589986 -0.6741149 -1.1163339 A104 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.2313867
405 1.1642231 -0.8904536 0.1512706 1.3676416 -0.6741149 -1.1163339 A301 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.4148139
406 -0.0480964 -0.8904536 -0.7758559 -0.7589986 0.4307274 -1.1163339 A165 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3532435
417 -0.3858139 -0.8904536 -0.6356183 -0.0501185 -0.6741149 -1.1163339 A142 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3325637
424 0.4801285 -0.0817113 -0.6356183 -0.0501185 0.4307274 -1.1163339 A261 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3953408
425 0.3242589 -0.0817113 -0.6356183 -0.0501185 -0.6741149 -1.1163339 A215 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.2711109
430 0.1337515 -1.2710382 -0.2850242 -0.0501185 -0.6741149 -1.1163339 A201 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.3910610
437 1.0170128 -0.8904536 -0.6356183 -0.0501185 2.6404120 -1.1163339 A343 C360 0.2356188 -0.4603485 -0.3744382 -0.4107768 2.6404120 0.5948051 0.5907461
446 0.6602445 -0.8904536 -0.6550957 1.3676416 0.4307274 -1.1163339 A345 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.6451381
452 0.3069400 -0.8904536 -0.6356183 -0.0501185 -0.6741149 -1.1163339 A187 C404 0.0640661 -0.3965677 -0.7815408 -0.3982964 -0.4164485 -1.4161834 0.2980627
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991 -0.7321909 -0.0817113 -1.1926732 -1.1134387 -0.6741149 1.0212337 A50 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2995067
992 -1.0716404 -0.0817113 -0.9472574 -0.7589986 -0.6741149 1.0212337 A51 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.2514187
994 3.9421665 -0.8904536 2.6755476 1.3676416 -0.6741149 1.0212337 A423 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 1.0198285
996 0.3918024 -0.8904536 0.0499878 -0.0501185 -0.6741149 1.0212337 A189 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.1784923
1008 0.6429257 0.6794579 -0.2850242 -0.0501185 2.6404120 1.0212337 A336 C360 0.2356188 -0.4603485 -0.3744382 -0.4107768 2.6404120 0.5948051 0.4039357
1011 0.4783966 -0.0817113 -1.1926732 -0.7589986 -0.6741149 1.0212337 A128 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.3931991
1012 -0.6109590 -1.2710382 -0.9472574 -0.7589986 2.6404120 1.0212337 A1 C360 0.2356188 -0.4603485 -0.3744382 -0.4107768 2.6404120 0.5948051 0.5007895
1013 -0.0740747 0.6794579 -0.6356183 -0.0501185 0.4307274 1.0212337 A247 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.2503772
1018 -0.7408504 -0.8904536 -1.1926732 -1.1134387 0.4307274 1.0212337 A15 C414 -0.4728276 -0.8354472 -0.4305269 -0.4820923 0.4307274 0.6016920 0.3560106
1020 -0.9053794 -0.8904536 -0.6356183 -0.7589986 -0.6741149 1.0212337 A72 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1838114
1036 1.0862882 0.6794579 -0.2850242 -0.0501185 2.6404120 1.0212337 A357 C96 2.0782294 0.7478725 0.1122044 0.7127714 2.6404120 0.5611990 0.4467515
1038 1.3529985 0.6794579 0.4940736 -0.0501185 0.4307274 1.0212337 A297 C219 1.9755430 0.5864499 0.2031375 -0.2014525 0.1203785 0.5809108 0.3180824
1039 2.2120134 -0.0817113 0.1512706 -0.0501185 -0.6741149 1.0212337 A257 C219 1.9755430 0.5864499 0.2031375 -0.2014525 0.1203785 0.5809108 0.3904415
1051 0.6446576 -1.2710382 0.4940736 1.3676416 -0.6741149 1.0212337 A290 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.2400317
1052 0.1337515 0.6794579 -0.6356183 -0.0501185 0.4307274 1.0212337 A247 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.2157395
1067 -1.2604158 -1.2710382 -1.1926732 -1.1134387 0.4307274 1.0212337 A15 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.3324035
1076 1.3443391 -0.8904536 0.4940736 1.3676416 -0.6741149 1.0212337 A299 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.2232783
1090 -2.0241771 -0.8904536 -1.2978514 -1.1134387 -0.6741149 1.0212337 A5 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.3023442
1097 0.6533170 -0.8904536 0.4940736 1.3676416 -0.6741149 1.0212337 A288 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.1751576
1112 -0.5607343 -0.8904536 -1.1926732 -1.1134387 -0.6741149 1.0212337 A48 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.2117200
1115 0.1406791 0.6794579 -1.1420319 -0.7589986 -0.6741149 1.0212337 A155 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2961620
1125 -1.2517564 -0.8904536 -1.1926732 -1.1134387 -0.6741149 1.0212337 A32 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1624117
1130 0.8247736 -1.2710382 0.4940736 1.3676416 -0.6741149 1.0212337 A290 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.2100123
1138 -1.2448289 -0.8904536 -1.1030770 -0.7589986 -0.6741149 1.0212337 A47 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1137335
1141 -0.3858139 -1.2710382 0.0499878 -0.0501185 -0.6741149 1.0212337 A159 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.2066937
1145 3.0848834 0.6794579 0.1434796 -0.0501185 2.6404120 1.0212337 A394 C96 2.0782294 0.7478725 0.1122044 0.7127714 2.6404120 0.5611990 0.3882114
1155 3.2511444 0.6794579 0.3382540 1.3676416 2.6404120 1.0212337 A413 C96 2.0782294 0.7478725 0.1122044 0.7127714 2.6404120 0.5611990 0.4303807
1160 -1.0716404 0.6794579 -1.1030770 -0.7589986 -0.6741149 1.0212337 A67 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2782722
1172 1.3374115 -0.0817113 0.4940736 1.3676416 -0.6741149 1.0212337 A333 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.3344434
1174 -0.3511762 0.6794579 -0.7914378 -0.7589986 -0.6741149 1.0212337 A137 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.1729719
1177 3.7707099 -0.0817113 2.6755476 1.3676416 -0.6741149 1.0212337 A423 C55 1.4810668 0.0181922 2.3175726 2.6287019 0.1225346 -0.2170130 1.0072463
1187 0.8334330 -0.8904536 -0.2655468 1.3676416 0.4307274 1.0212337 A323 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.3620957
1188 -0.5590024 -0.8904536 -0.7836469 -0.0501185 0.4307274 1.0212337 A172 C414 -0.4728276 -0.8354472 -0.4305269 -0.4820923 0.4307274 0.6016920 0.2243028
1196 1.4309333 -0.8904536 0.4940736 1.3676416 -0.6741149 1.0212337 A299 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.2377106
1197 0.6602445 -0.0817113 -0.7135281 -0.7589986 -0.6741149 1.0212337 A128 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.3868376
1200 -0.8118576 -0.8904536 -0.7135281 -0.7589986 -0.6741149 1.0212337 A72 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1656158
1206 -0.5607343 -1.2710382 -0.7758559 -0.0501185 -0.6741149 1.0212337 A79 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.2660686
1218 1.0066215 0.6794579 0.1434796 -0.0501185 0.4307274 1.0212337 A297 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.2771260
1220 -0.3511762 -0.8904536 -0.6356183 -0.0501185 0.4307274 1.0212337 A172 C414 -0.4728276 -0.8354472 -0.4305269 -0.4820923 0.4307274 0.6016920 0.2055441
1221 1.1728825 -0.0817113 0.4940736 1.3676416 -0.6741149 1.0212337 A333 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.3070218
1228 0.1250921 0.6794579 -0.7758559 -0.7589986 0.4307274 1.0212337 A173 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.3213397
1242 -0.3858139 -0.8904536 -0.7758559 -0.7589986 -0.6741149 1.0212337 A88 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1265840
1247 2.3852019 0.6794579 0.1512706 -0.0501185 -0.6741149 1.0212337 A300 C219 1.9755430 0.5864499 0.2031375 -0.2014525 0.1203785 0.5809108 0.3234473
1253 -0.4741401 -0.0817113 -1.1926732 -1.1134387 -0.6741149 1.0212337 A91 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2650090
1254 0.2445922 -0.8904536 -0.2850242 -0.0501185 2.6404120 1.0212337 A255 C360 0.2356188 -0.4603485 -0.3744382 -0.4107768 2.6404120 0.5948051 0.2192632
1259 0.9113679 0.6794579 0.0499878 -0.0501185 -0.6741149 1.0212337 A239 C326 0.4078813 0.4460352 -0.0758046 -0.2045827 -0.6741149 0.6597676 0.2297720
1269 0.1337515 -0.0817113 -0.2850242 -0.0501185 0.4307274 0.3221550 A238 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.2205069
1270 -0.2056979 -0.8904536 -1.1420319 -0.7589986 -0.6741149 0.3221550 A98 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1522240
1277 0.1337515 -0.8904536 0.0499878 -0.0501185 -0.6741149 0.3221550 A188 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.0905453
1282 -1.2604158 -1.2710382 -1.1926732 -1.1134387 -0.6741149 0.3221550 A27 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.2370416
1283 0.4870561 -0.0817113 -0.2850242 -0.0501185 0.4307274 0.3221550 A252 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.2420173
1285 -0.3788864 0.6794579 -0.9472574 -0.7589986 -0.6741149 0.3221550 A125 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.1739817
1287 0.6515851 -0.0817113 0.0499878 -0.0501185 -0.6741149 0.3221550 A221 C326 0.4078813 0.4460352 -0.0758046 -0.2045827 -0.6741149 0.6597676 0.2315532
1288 -0.8118576 -0.0817113 -0.7836469 -0.7589986 -0.6741149 0.3221550 A94 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2307387
1298 -0.5001183 0.6794579 -0.7914378 -0.7589986 0.4307274 0.3221550 A197 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2927816
1302 -0.4221835 -1.2710382 -1.1420319 -0.7589986 -0.6741149 0.3221550 A60 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1520934
1303 -0.7079445 -0.0817113 -0.7914378 -0.7589986 0.4307274 0.3221550 A149 C414 -0.4728276 -0.8354472 -0.4305269 -0.4820923 0.4307274 0.6016920 0.3177012
1305 0.0454254 -0.8904536 0.0499878 -0.0501185 -0.6741149 0.3221550 A188 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.0758243
1310 -1.4249449 -1.2710382 -0.9472574 -0.7589986 0.4307274 0.3221550 A76 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.3429802
1311 -0.0325094 -0.0817113 -0.7135281 -0.0501185 0.4307274 0.3221550 A191 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.3196344
1320 -0.9053794 -0.8904536 -1.1926732 -1.1134387 -0.6741149 0.3221550 A45 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.2339490
1329 -0.6473286 -1.2710382 -0.7758559 -0.7589986 -0.6741149 0.3221550 A87 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1285448
1336 3.2511444 0.6794579 0.3382540 1.3676416 2.6404120 0.3221550 A426 C96 2.0782294 0.7478725 0.1122044 0.7127714 2.6404120 0.5611990 0.3935489
1348 -0.9053794 -1.2710382 -0.7758559 -0.7589986 -0.6741149 0.3221550 A55 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1715532
1367 0.4350995 -0.8904536 -0.6550957 -0.0501185 -0.6741149 0.3221550 A175 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.2582839
1375 -0.3009516 -0.8904536 -0.7758559 -0.7589986 -0.6741149 0.3221550 A109 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1055158
1377 0.0454254 -0.0817113 -0.7758559 -0.7589986 -0.6741149 0.3221550 A147 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2708561
1382 0.6256068 -0.8904536 -0.2850242 -0.7589986 -0.6741149 0.3221550 A144 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.3224593
1383 0.2186139 -0.8904536 -1.1420319 -0.7589986 -0.6741149 0.3221550 A98 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.2229426
1387 1.6907161 0.6794579 0.0421969 1.3676416 0.4307274 0.3221550 A355 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.3025392
1388 0.1926356 -0.8904536 -0.2850242 -0.0501185 2.6404120 0.3221550 A255 C360 0.2356188 -0.4603485 -0.3744382 -0.4107768 2.6404120 0.5948051 0.1993018
1390 -1.0872273 -0.8904536 -1.1926732 -1.1134387 0.4307274 0.3221550 A40 C414 -0.4728276 -0.8354472 -0.4305269 -0.4820923 0.4307274 0.6016920 0.3904060
1393 0.4853242 -0.0817113 -0.7135281 -0.7589986 -0.6741149 0.3221550 A147 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.3545605
1396 -1.0716404 -1.2710382 -1.1420319 -0.7589986 -0.6741149 0.3221550 A36 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.2251638
1413 -0.8984519 0.6794579 -0.9472574 -0.7589986 -0.6741149 0.3221550 A125 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2203138
1414 -2.1107713 -0.8904536 -1.2978514 -1.1134387 -0.6741149 0.3221550 A14 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.3791820
1434 -0.6473286 -0.8904536 -1.1926732 -1.1134387 -0.6741149 0.3221550 A64 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1909405
1440 0.4714691 -0.0817113 0.0499878 -0.0501185 -0.6741149 0.3221550 A221 C326 0.4078813 0.4460352 -0.0758046 -0.2045827 -0.6741149 0.6597676 0.2015339
1441 4.8167683 0.6794579 0.4356413 -0.0501185 2.6404120 0.3221550 A394 C96 2.0782294 0.7478725 0.1122044 0.7127714 2.6404120 0.5611990 0.6887207
1443 1.3374115 -0.0817113 0.4473277 1.3676416 0.4307274 0.3221550 A347 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.3305615
1451 1.2577448 -0.8904536 0.4473277 1.3676416 -0.6741149 0.3221550 A309 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.1505595
1453 0.6446576 -1.2710382 0.4473277 1.3676416 -0.6741149 0.3221550 A285 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.1817453
1454 -0.7772199 -0.8904536 -0.9472574 -0.7589986 -0.6741149 0.3221550 A92 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1126131
1455 1.3460710 0.6794579 0.0421969 1.3676416 0.4307274 0.3221550 A355 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.2450983
1459 0.8178461 -0.0817113 -0.2850242 -0.0501185 0.4307274 0.3221550 A252 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.2971490
1461 1.1798100 -0.0817113 -0.3629340 -0.0501185 0.4307274 0.3221550 A252 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.3704613
1480 1.6041218 -0.0817113 0.4473277 1.3676416 -0.6741149 0.3221550 A326 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.3206087
1483 1.3460710 0.6794579 0.4473277 1.3676416 -0.6741149 0.3221550 A354 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.2430285
1486 -0.2143573 0.6794579 -1.1926732 -1.1134387 -0.6741149 0.3221550 A140 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2728719
1491 1.5106000 0.6794579 0.4473277 1.3676416 0.4307274 0.3221550 A373 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.2325647
1496 0.8178461 -0.8904536 0.4473277 1.3676416 0.4307274 0.3221550 A315 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.2046355
1497 1.1728825 -0.0817113 0.4473277 1.3676416 -0.6741149 0.3221550 A326 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.2487355
1500 -0.5676619 -0.8904536 -0.7758559 -0.7589986 -0.6741149 0.3221550 A92 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.0793166
1502 0.6533170 -0.8904536 0.4473277 1.3676416 -0.6741149 0.3221550 A294 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.1168713
1504 -0.2126255 -0.8904536 -0.2850242 -0.0501185 0.4307274 0.3221550 A181 C414 -0.4728276 -0.8354472 -0.4305269 -0.4820923 0.4307274 0.6016920 0.1953703
1507 5.5095223 0.6794579 3.0650965 4.2031619 2.6404120 0.8195764 A440 B12 5.5095223 0.6794579 3.0650965 4.2031619 2.6404120 0.4969247 0.0537753
1508 -0.2212849 -0.8904536 -0.7758559 -0.7589986 0.4307274 0.8195764 A122 C414 -0.4728276 -0.8354472 -0.4305269 -0.4820923 0.4307274 0.6016920 0.1911115
1510 -0.0394370 -0.8904536 -0.7836469 -0.7589986 2.6404120 0.8195764 A11 C360 0.2356188 -0.4603485 -0.3744382 -0.4107768 2.6404120 0.5948051 0.2812271
1511 0.6446576 0.6794579 0.0499878 -0.0501185 0.4307274 0.8195764 A277 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.1676072
1514 -0.8811330 -1.2710382 -1.1420319 -0.7589986 -0.6741149 0.8195764 A39 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1740115
1515 0.2186139 -0.0817113 -0.2850242 -0.0501185 0.4307274 0.8195764 A238 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.1781350
1519 -0.0480964 -0.8904536 0.0499878 -0.0501185 -0.6741149 0.8195764 A168 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.0756235
1525 2.0215061 0.6794579 3.7273297 -0.0501185 -0.6741149 0.8195764 A410 C219 1.9755430 0.5864499 0.2031375 -0.2014525 0.1203785 0.5809108 0.8079427
1527 -1.4249449 -0.8904536 -0.7836469 -0.7589986 -0.6741149 0.8195764 A54 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1034432
1528 0.9113679 -1.2710382 0.4473277 1.3676416 -0.6741149 0.8195764 A290 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.1731466
1530 0.1337515 -0.8904536 0.0499878 -0.0501185 -0.6741149 0.8195764 A189 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.1018743
1538 -0.8984519 0.6794579 -0.9472574 -0.7589986 -0.6741149 0.8195764 A125 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.1898280
1539 -1.4249449 -1.2710382 -1.1926732 -1.1134387 -0.6741149 0.8195764 A18 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1781120
1555 0.2532516 -0.8904536 -0.7836469 -0.7589986 -0.6741149 0.8195764 A106 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1981869
1558 0.6446576 -1.2710382 0.4473277 1.3676416 -0.6741149 0.8195764 A290 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.1986311
1563 0.2705704 -0.8904536 -1.1420319 -0.7589986 -0.6741149 0.8195764 A97 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.2332044
1570 -0.0480964 -0.0817113 -0.7758559 -0.7589986 -0.6741149 0.8195764 A128 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2247832
1576 -0.9053794 -1.2710382 -0.7758559 -0.7589986 -0.6741149 0.8195764 A56 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1536080
1577 -0.2126255 0.6794579 -0.2850242 -0.7589986 0.4307274 0.8195764 A173 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.2622111
1581 -0.3944734 0.6794579 -1.1926732 -1.1134387 -0.6741149 0.8195764 A114 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2123667
1586 0.1320196 -0.8904536 0.0499878 -0.0501185 -0.6741149 0.8195764 A189 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.1015856
1590 1.6041218 0.6794579 0.4473277 1.3676416 -0.6741149 0.8195764 A353 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.2438723
1594 0.3069400 -0.0817113 -0.2850242 -0.7589986 2.6404120 0.8195764 A320 C360 0.2356188 -0.4603485 -0.3744382 -0.4107768 2.6404120 0.5948051 0.1853942
1596 -0.7252634 -0.8904536 -1.1420319 -0.7589986 -0.6741149 0.8195764 A61 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1380184
1602 -0.9937055 -1.2710382 -1.1926732 -1.1134387 -0.6741149 0.8195764 A18 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1985897
1603 0.3918024 -0.8904536 0.0499878 -0.0501185 -0.6741149 0.8195764 A189 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.1448827
1617 0.8438243 0.6794579 0.5135511 -0.0501185 0.4307274 0.8195764 A277 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.2780622
1624 -1.5981334 -1.2710382 -0.9472574 -0.7589986 -0.6741149 0.8195764 A22 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1311740
1626 -0.2126255 -0.0817113 -0.7758559 -0.7589986 -0.6741149 0.8195764 A128 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.1973617
1633 0.1320196 -0.0817113 -0.7758559 -0.7589986 -0.6741149 0.8195764 A128 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2548026
1642 0.9633244 -0.8904536 -0.2850242 -0.7589986 -0.6741149 0.8195764 A144 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.3900745
1645 -0.7079445 -0.0817113 -0.7914378 -0.7589986 0.4307274 0.8195764 A149 C414 -0.4728276 -0.8354472 -0.4305269 -0.4820923 0.4307274 0.6016920 0.3074258
1649 -0.7495098 -0.8904536 -0.2850242 -0.7589986 0.4307274 0.8195764 A141 C414 -0.4728276 -0.8354472 -0.4305269 -0.4820923 0.4307274 0.6016920 0.1619970
1659 1.6907161 0.6794579 0.4473277 1.3676416 -0.6741149 0.8195764 A353 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.2583046
1669 1.5106000 0.6794579 0.4473277 1.3676416 -0.6741149 0.8195764 A353 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.2282853
1670 0.9113679 -0.8904536 0.4473277 1.3676416 -0.6741149 0.8195764 A288 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.1097159
1671 0.8853896 0.6794579 -0.6550957 -0.7589986 0.4307274 0.8195764 A262 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.3540595
1681 0.3069400 0.6794579 -0.2850242 -0.0501185 0.4307274 0.8195764 A247 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.1151887
1683 -1.2604158 -1.2710382 -1.1926732 -1.1134387 -0.6741149 0.8195764 A18 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1541380
1688 -0.5520749 -0.0817113 -0.2850242 -0.7589986 -0.6741149 0.8195764 A132 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2400595
1692 0.0454254 -0.8904536 0.0499878 -0.0501185 -0.6741149 0.8195764 A168 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.0871532
1695 -0.5590024 0.6794579 -1.1926732 -1.1134387 -0.6741149 0.8195764 A95 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2047218
1697 -0.5590024 -1.2710382 -0.9472574 -0.7589986 2.6404120 0.8195764 A11 C360 0.2356188 -0.4603485 -0.3744382 -0.4107768 2.6404120 0.5948051 0.4585205
1704 2.4787237 0.6794579 0.1434796 -0.0501185 0.4307274 0.8195764 A329 C219 1.9755430 0.5864499 0.2031375 -0.2014525 0.1203785 0.5809108 0.2260325
1728 -1.4180174 -0.8904536 -0.7836469 -0.7589986 -0.6741149 0.8195764 A54 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1022886
1729 -0.3858139 0.6794579 -0.2850242 -0.7589986 -0.6741149 0.8195764 A154 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2179917
1731 0.7901359 -0.8904536 -0.6550957 -0.0501185 -0.6741149 0.8195764 A175 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.3287856
1742 -0.3944734 -0.8904536 -0.7836469 -0.7589986 -0.6741149 0.8195764 A99 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.0902327
1745 1.3374115 -0.0817113 0.4473277 1.3676416 -0.6741149 0.8195764 A333 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.2930428
1756 1.6976436 0.6794579 0.1434796 1.3676416 0.4307274 0.8195764 A359 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.2446486
1759 -0.7425822 -0.8904536 -0.6356183 -0.7589986 -0.6741149 0.8195764 A83 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1334453
1771 -0.1277631 -0.8904536 -0.7758559 -0.7589986 -0.6741149 0.8195764 A106 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1359830
1772 -1.1755535 -1.2710382 -0.7836469 -0.7589986 -0.6741149 0.8195764 A35 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1072805
1774 0.8334330 -0.8904536 -0.6745732 -0.7589986 -0.6741149 0.8195764 A144 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.3130628
1784 -1.3314231 -1.2710382 -0.7836469 -0.7589986 -0.6741149 0.8195764 A35 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1015238
1798 -1.5981334 -1.2710382 -0.7836469 -0.7589986 -0.6741149 0.4969247 A37 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1997508
1800 -0.9140388 -1.2710382 -0.7836469 -0.7589986 -0.6741149 0.4969247 A55 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1425697
1811 -0.4395024 -1.2710382 -1.1420319 -0.7589986 -0.6741149 0.4969247 A60 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1200787
1813 -0.0480964 -0.0817113 -1.1926732 -1.1134387 -0.6741149 0.4969247 A91 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.3037644
1818 2.2968758 0.6794579 -0.2850242 1.3676416 2.6404120 0.4969247 A413 C96 2.0782294 0.7478725 0.1122044 0.7127714 2.6404120 0.5611990 0.2339057
1819 -0.5070459 0.6794579 -0.2850242 -0.7589986 0.4307274 0.4969247 A233 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.3103811
1824 -0.6802344 0.6794579 -0.2850242 -0.7589986 -0.6741149 0.4969247 A154 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2304664
1826 0.0454254 -0.0817113 -0.7758559 -0.7589986 -0.6741149 0.4969247 A147 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2417278
1832 -0.2056979 -0.8904536 -1.1420319 -0.7589986 -0.6741149 0.4969247 A98 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1230957
1845 -0.9850461 -1.2710382 -1.1420319 -0.7589986 -0.6741149 0.4969247 A36 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1865353
1858 0.4870561 0.6794579 0.0421969 -0.0501185 0.4307274 0.4969247 A277 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.1391417
1865 -0.0861979 -0.8904536 -0.7836469 -0.7589986 -0.6741149 0.4969247 A118 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1108814
1871 0.8091866 0.6794579 0.5135511 -0.0501185 -0.6741149 0.4969247 A253 C326 0.4078813 0.4460352 -0.0758046 -0.2045827 -0.6741149 0.6597676 0.2568985
1872 -0.3009516 0.6794579 -1.1926732 -1.1134387 -0.6741149 0.4969247 A112 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2293112
1875 0.1164327 0.6794579 -0.2850242 -0.0501185 0.4307274 0.4969247 A247 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.1256840
1876 0.2532516 -0.8904536 -0.7836469 -0.7589986 -0.6741149 0.4969247 A118 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1674563
1877 -0.6473286 -1.2710382 -0.7758559 -0.7589986 -0.6741149 0.4969247 A87 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.0994165
1889 -0.7252634 -0.8904536 -0.7135281 -0.7589986 -0.6741149 0.4969247 A92 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.0868432
1890 0.3831430 -0.0817113 -0.2850242 -0.0501185 2.6404120 0.4969247 A320 C360 0.2356188 -0.4603485 -0.3744382 -0.4107768 2.6404120 0.5948051 0.1790190
1892 -0.9053794 -1.2710382 -0.7758559 -0.7589986 -0.6741149 0.4969247 A55 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1424249
1897 1.6041218 -0.0817113 0.4473277 1.3676416 -0.6741149 0.4969247 A326 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.2914804
1901 -0.0567558 -1.2710382 0.4473277 -0.0501185 -0.6741149 0.4969247 A160 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.1438113
1910 0.4853242 -0.0817113 -0.3629340 -0.0501185 0.4307274 0.4969247 A252 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.2255854
1919 -0.8118576 -0.0817113 -0.6550957 -0.7589986 0.4307274 0.4969247 A149 C414 -0.4728276 -0.8354472 -0.4305269 -0.4820923 0.4307274 0.6016920 0.2831681
1922 2.0301655 0.6794579 0.4473277 1.3676416 -0.6741149 0.4969247 A368 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.3279160
1929 0.2445922 -0.8904536 -0.6550957 -0.0501185 -0.6741149 0.4969247 A175 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.1974044
1930 -0.2922922 -0.8904536 -0.7836469 -0.7589986 -0.6741149 0.4969247 A109 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.0765323
1937 -0.0480964 -0.8904536 -0.7758559 -0.7589986 -0.6741149 0.4969247 A118 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1185301
1940 0.2186139 0.6794579 -0.7758559 -0.7589986 -0.6741149 0.4969247 A179 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2382820
1941 -0.9053794 -0.8904536 -0.2850242 -0.7589986 0.4307274 0.4969247 A141 C414 -0.4728276 -0.8354472 -0.4305269 -0.4820923 0.4307274 0.6016920 0.1691224
1944 0.1406791 0.6794579 -1.1420319 -0.7589986 -0.6741149 0.4969247 A140 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.2639100
1965 2.0457525 0.6794579 0.4434322 -0.7589986 0.4307274 0.4969247 A329 C219 1.9755430 0.5864499 0.2031375 -0.2014525 0.1203785 0.5809108 0.2258989
1971 -1.2604158 -1.2710382 -1.1926732 -1.1134387 0.4307274 0.4969247 A15 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.3656806
1975 -0.8984519 -1.2710382 -0.7836469 -0.7589986 -0.6741149 0.4969247 A55 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1399719
1979 0.4714691 -0.0817113 -0.7758559 -0.7589986 -0.6741149 0.4969247 A147 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.3127351
1986 -0.3858139 -1.2710382 0.0499878 -0.0501185 -0.6741149 0.4969247 A160 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.1326269
1998 0.1337515 0.6794579 -0.2850242 -0.0501185 0.4307274 0.4969247 A247 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.1227975
2007 0.8178461 -0.8904536 0.0499878 -0.0501185 -0.6741149 0.4969247 A188 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.1754328
2010 1.0914839 0.6794579 -0.6550957 -0.7589986 0.4307274 0.4969247 A262 C297 0.2458726 0.5046167 -0.1059150 -0.1622064 0.4307274 0.6555503 0.3875085
2014 -1.2517564 -0.8904536 -0.7836469 -0.7589986 -0.6741149 0.4969247 A63 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1346877
2015 0.9113679 -1.2710382 0.4473277 1.3676416 -0.6741149 0.4969247 A290 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.1271325
2019 -1.2517564 -0.8904536 -0.7836469 -0.7589986 -0.6741149 0.4969247 A63 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1346877
2020 -0.7408504 -1.2710382 -1.1926732 -1.1134387 -0.6741149 0.4969247 A27 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.2133495
2023 -0.5676619 -0.0817113 -1.1926732 -1.1134387 0.4307274 0.4969247 A68 C434 -0.4996726 0.3958051 -0.8430922 -0.8445203 -0.5645193 0.6623233 0.3874417
2025 -0.8811330 -1.2710382 -1.1420319 -0.7589986 -0.6741149 0.4969247 A60 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1692164
2040 0.4108531 -0.8904536 0.5135511 -0.0501185 -0.6741149 0.4969247 A202 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.1846652
2048 -0.2576545 -0.8904536 -0.2850242 -0.7589986 -0.6741149 0.7120258 A127 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1782146
2054 -0.7166040 -1.2710382 -1.1420319 -0.7589986 -0.6741149 0.7120258 A57 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1546005
2056 -1.1149375 -1.2710382 -0.7836469 -0.7589986 -0.6741149 0.7120258 A55 C512 -1.2707584 -1.0397430 -0.9098567 -0.8315183 -0.5949957 0.8589108 0.1353083
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2113 -0.3355893 -1.2710382 -0.9472574 -0.7589986 -0.6741149 0.7120258 A84 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1177407
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2118 0.1250921 -0.8904536 -0.7758559 -0.7589986 -0.6741149 0.7120258 A118 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.1602004
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2134 1.3460710 0.6794579 -0.2850242 1.3676416 0.4307274 0.7120258 A355 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.2395454
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2146 -0.2749733 -0.8904536 -0.7836469 -0.7589986 -0.6741149 0.7120258 A99 C471 -0.5129045 -0.9728948 -0.8664462 -0.7547916 -0.6741149 0.5660586 0.0922243
2149 3.0779559 0.6794579 2.2859986 1.3676416 -0.6741149 0.7120258 A423 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.7780313
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2161 0.2272733 0.6794579 -0.2850242 -0.7589986 -0.6741149 0.7120258 A195 C326 0.4078813 0.4460352 -0.0758046 -0.2045827 -0.6741149 0.6597676 0.2049874
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4210 1.3339478 -0.8904536 -0.5577085 -0.7589986 2.6404120 0.0398347 A311 C360 0.2356188 -0.4603485 -0.3744382 -0.4107768 2.6404120 0.5948051 0.4358161
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4272 0.7364475 0.6794579 1.1952617 1.3676416 -0.6741149 0.3490426 A327 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.4568269
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4349 0.5632590 -0.8904536 1.1952617 1.3676416 -0.6741149 0.3490426 A313 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.2520553
4351 0.5823097 0.6794579 1.1952617 1.3676416 -0.6741149 0.3490426 A327 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.4825165
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4441 1.3443391 2.2969425 1.1952617 1.3676416 -0.6741149 0.3490426 A388 C147 1.3221312 0.9897072 0.3646278 1.3676416 -0.0080377 0.6973599 0.5290786
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4449 1.4309333 -0.8904536 2.2859986 2.7854017 -0.6741149 0.3490426 A404 C55 1.4810668 0.0181922 2.3175726 2.6287019 0.1225346 -0.2170130 0.4182930
4450 -0.2836327 2.2969425 -0.7758559 -0.7589986 -0.6741149 0.3490426 A19 C301 0.3539798 2.2969425 -0.1275540 -0.2934206 -0.2808659 0.8171839 0.4354804
4458 1.5261870 0.6794579 2.2859986 1.3676416 0.4307274 0.3490426 A402 C55 1.4810668 0.0181922 2.3175726 2.6287019 0.1225346 -0.2170130 0.4788781
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4471 0.3069400 -0.8904536 1.1952617 1.3676416 -0.6741149 0.3490426 A313 C228 0.8544662 -0.8230415 0.4195786 1.3676416 -0.4672508 0.5202082 0.2947752
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5057 -0.5676619 -0.8904536 0.4473277 -0.0501185 -0.6741149 -0.5382496 A198 C384 -0.0359246 -0.9572228 0.0505756 -0.1222502 -0.6547317 0.5368788 0.3603170
5060 0.3554328 -0.0817113 1.1952617 1.3676416 0.4307274 -0.5382496 A364 C130 0.2826529 -0.0067137 1.6381330 0.9923522 0.2097590 -0.6177263 0.2110639
5064 0.1337515 -0.0817113 1.1952617 1.3676416 0.4307274 -0.5382496 A364 C130 0.2826529 -0.0067137 1.6381330 0.9923522 0.2097590 -0.6177263 0.2237508
5084 0.0627443 -0.8904536 1.1952617 1.3676416 0.4307274 -0.5382496 A351 C130 0.2826529 -0.0067137 1.6381330 0.9923522 0.2097590 -0.6177263 0.3703757
5096 -0.0394370 -0.8904536 1.1952617 1.3676416 0.4307274 -0.5382496 A351 C130 0.2826529 -0.0067137 1.6381330 0.9923522 0.2097590 -0.6177263 0.3874059
5106 -0.4239154 0.6794579 0.4473277 -0.0501185 -0.6741149 -0.5382496 A246 C306 -0.7716661 0.5467115 0.2755179 -0.2228202 -0.1702066 -0.7871317 0.2629665
5110 -1.5219304 -0.8904536 0.0421969 -0.7589986 -0.6741149 -0.5382496 A111 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.2482625
5113 -0.5676619 -0.8904536 0.4473277 -0.0501185 0.4307274 -0.5382496 A227 C414 -0.4728276 -0.8354472 -0.4305269 -0.4820923 0.4307274 0.6016920 0.4332684
5116 -1.0006331 0.6794579 -0.7758559 -0.7589986 -0.6741149 -0.5382496 A129 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.3400136
5129 -1.0214157 -0.0817113 0.0577788 -0.7589986 2.6404120 -0.5382496 A295 C142 0.1328959 0.6627507 0.4814828 -0.0248014 2.6404120 -0.9712527 0.5816130
5130 -1.0629809 0.6794579 -0.7758559 -0.7589986 -0.6741149 -0.5382496 A129 C478 -1.1829114 -0.7922801 -0.6999883 -0.7557764 -0.5234546 -0.6945646 0.3296222

hist(sorted_df$diff, breaks = 30, col = "blue", main = "Mean Absolute Difference", xlab = "Difference")
Figure 22: Mean Absolute Difference

Figure 22: Mean Absolute Difference

7 Executive Summary

8 References

  1. Topology Preserving Maps : https://users.ics.aalto.fi/jhollmen/dippa/node9.html#

  2. Vector Quantization : https://en.wikipedia.org/wiki/Vector_quantization

  3. K-means : https://en.wikipedia.org/wiki/K-means_clustering

  4. Sammon’s Projection : http://en.wikipedia.org/wiki/Sammon_mapping

  5. Voronoi Tessellations : http://en.wikipedia.org/wiki/Centroidal_Voronoi_tessellation